Whakaoti i te 8x+16+8/x+2*1/x-2=8x^2-25/x-2

$$8 x + 16 + \frac { 8 } { x + 2 } \cdot \frac { 1 } { x - 2 } = \frac { 8 x ^ { 2 } - 25 } { x - 2 }$$

Whakaoti mō x

$$x=-\frac{6}{7}\approx -0.857142857$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -2,2 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te \left(x-2\right)\left(x+2\right), arā, te tauraro pātahi he tino iti rawa te kitea o x+2,x-2.

$$8x\left(x-2\right)\left(x+2\right)+\left(x-2\right)\left(x+2\right)\times 16+\left(x-2\right)\times 8\times \frac{1}{x-2}=\left(x+2\right)\left(8x^{2}-25\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 8x ki te x-2.

$$\left(8x^{2}-16x\right)\left(x+2\right)+\left(x-2\right)\left(x+2\right)\times 16+\left(x-2\right)\times 8\times \frac{1}{x-2}=\left(x+2\right)\left(8x^{2}-25\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 8x^{2}-16x ki te x+2 ka whakakotahi i ngā kupu rite.

$$8x^{3}-32x+\left(x-2\right)\left(x+2\right)\times 16+\left(x-2\right)\times 8\times \frac{1}{x-2}=\left(x+2\right)\left(8x^{2}-25\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x-2 ki te x+2 ka whakakotahi i ngā kupu rite.

$$8x^{3}-32x+\left(x^{2}-4\right)\times 16+\left(x-2\right)\times 8\times \frac{1}{x-2}=\left(x+2\right)\left(8x^{2}-25\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x^{2}-4 ki te 16.

$$8x^{3}-32x+16x^{2}-64+\left(x-2\right)\times 8\times \frac{1}{x-2}=\left(x+2\right)\left(8x^{2}-25\right)$$

Tuhia te \left(x-2\right)\times \frac{1}{x-2} hei hautanga kotahi.

$$8x^{3}-32x+16x^{2}-64+\frac{x-2}{x-2}\times 8=\left(x+2\right)\left(8x^{2}-25\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x+2 ki te 8x^{2}-25.

$$8x^{3}-32x+16x^{2}-64+\frac{x-2}{x-2}\times 8=8x^{3}-25x+16x^{2}-50$$

Tuhia te \frac{x-2}{x-2}\times 8 hei hautanga kotahi.

$$8x^{3}-32x+16x^{2}-64+\frac{\left(x-2\right)\times 8}{x-2}=8x^{3}-25x+16x^{2}-50$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 8x^{3}-32x+16x^{2}-64 ki te \frac{x-2}{x-2}.

$$\frac{\left(8x^{3}-32x+16x^{2}-64\right)\left(x-2\right)}{x-2}+\frac{\left(x-2\right)\times 8}{x-2}=8x^{3}-25x+16x^{2}-50$$

Tā te mea he rite te tauraro o \frac{\left(8x^{3}-32x+16x^{2}-64\right)\left(x-2\right)}{x-2} me \frac{\left(x-2\right)\times 8}{x-2}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\left(8x^{3}-32x+16x^{2}-64\right)\left(x-2\right)+\left(x-2\right)\times 8}{x-2}=8x^{3}-25x+16x^{2}-50$$

Mahia ngā whakarea i roto o \left(8x^{3}-32x+16x^{2}-64\right)\left(x-2\right)+\left(x-2\right)\times 8.

$$\frac{8x^{4}-16x^{3}-32x^{2}+64x+16x^{3}-32x^{2}-64x+128+8x-16}{x-2}=8x^{3}-25x+16x^{2}-50$$

Whakakotahitia ngā kupu rite i 8x^{4}-16x^{3}-32x^{2}+64x+16x^{3}-32x^{2}-64x+128+8x-16.

$$\frac{8x^{4}-64x^{2}+8x+112}{x-2}=8x^{3}-25x+16x^{2}-50$$

Tangohia te 8x^{3} mai i ngā taha e rua.

$$\frac{8x^{4}-64x^{2}+8x+112}{x-2}-8x^{3}=-25x+16x^{2}-50$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia -8x^{3} ki te \frac{x-2}{x-2}.

$$\frac{8x^{4}-64x^{2}+8x+112}{x-2}+\frac{-8x^{3}\left(x-2\right)}{x-2}=-25x+16x^{2}-50$$

Tā te mea he rite te tauraro o \frac{8x^{4}-64x^{2}+8x+112}{x-2} me \frac{-8x^{3}\left(x-2\right)}{x-2}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{8x^{4}-64x^{2}+8x+112-8x^{3}\left(x-2\right)}{x-2}=-25x+16x^{2}-50$$

Mahia ngā whakarea i roto o 8x^{4}-64x^{2}+8x+112-8x^{3}\left(x-2\right).

$$\frac{8x^{4}-64x^{2}+8x+112-8x^{4}+16x^{3}}{x-2}=-25x+16x^{2}-50$$

Whakakotahitia ngā kupu rite i 8x^{4}-64x^{2}+8x+112-8x^{4}+16x^{3}.

$$\frac{-64x^{2}+8x+112+16x^{3}}{x-2}=-25x+16x^{2}-50$$

Me tāpiri te 25x ki ngā taha e rua.

$$\frac{-64x^{2}+8x+112+16x^{3}}{x-2}+25x=16x^{2}-50$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 25x ki te \frac{x-2}{x-2}.

$$\frac{-64x^{2}+8x+112+16x^{3}}{x-2}+\frac{25x\left(x-2\right)}{x-2}=16x^{2}-50$$

Tā te mea he rite te tauraro o \frac{-64x^{2}+8x+112+16x^{3}}{x-2} me \frac{25x\left(x-2\right)}{x-2}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{-64x^{2}+8x+112+16x^{3}+25x\left(x-2\right)}{x-2}=16x^{2}-50$$

Mahia ngā whakarea i roto o -64x^{2}+8x+112+16x^{3}+25x\left(x-2\right).

$$\frac{-64x^{2}+8x+112+16x^{3}+25x^{2}-50x}{x-2}=16x^{2}-50$$

Whakakotahitia ngā kupu rite i -64x^{2}+8x+112+16x^{3}+25x^{2}-50x.

$$\frac{-39x^{2}-42x+112+16x^{3}}{x-2}=16x^{2}-50$$

Tangohia te 16x^{2} mai i ngā taha e rua.

$$\frac{-39x^{2}-42x+112+16x^{3}}{x-2}-16x^{2}=-50$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia -16x^{2} ki te \frac{x-2}{x-2}.

$$\frac{-39x^{2}-42x+112+16x^{3}}{x-2}+\frac{-16x^{2}\left(x-2\right)}{x-2}=-50$$

Tā te mea he rite te tauraro o \frac{-39x^{2}-42x+112+16x^{3}}{x-2} me \frac{-16x^{2}\left(x-2\right)}{x-2}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{-39x^{2}-42x+112+16x^{3}-16x^{2}\left(x-2\right)}{x-2}=-50$$

Mahia ngā whakarea i roto o -39x^{2}-42x+112+16x^{3}-16x^{2}\left(x-2\right).

$$\frac{-39x^{2}-42x+112+16x^{3}-16x^{3}+32x^{2}}{x-2}=-50$$

Whakakotahitia ngā kupu rite i -39x^{2}-42x+112+16x^{3}-16x^{3}+32x^{2}.

$$\frac{-7x^{2}-42x+112}{x-2}=-50$$

Me tāpiri te 50 ki ngā taha e rua.

$$\frac{-7x^{2}-42x+112}{x-2}+50=0$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 50 ki te \frac{x-2}{x-2}.

$$\frac{-7x^{2}-42x+112}{x-2}+\frac{50\left(x-2\right)}{x-2}=0$$

Tā te mea he rite te tauraro o \frac{-7x^{2}-42x+112}{x-2} me \frac{50\left(x-2\right)}{x-2}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{-7x^{2}-42x+112+50\left(x-2\right)}{x-2}=0$$

Mahia ngā whakarea i roto o -7x^{2}-42x+112+50\left(x-2\right).

$$\frac{-7x^{2}-42x+112+50x-100}{x-2}=0$$

Whakakotahitia ngā kupu rite i -7x^{2}-42x+112+50x-100.

$$\frac{-7x^{2}+8x+12}{x-2}=0$$

Tē taea kia ōrite te tāupe x ki 2 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x-2.

$$-7x^{2}+8x+12=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -7x^{2}+ax+bx+12. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=8 ab=-7\times 12=-84$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōrunga te a+b, he nui ake te uara pū o te tau tōrunga i tō te tōraro. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -84.

$$-1,84 -2,42 -3,28 -4,21 -6,14 -7,12$$

Tātaihia te tapeke mō ia takirua.

$$-1+84=83 -2+42=40 -3+28=25 -4+21=17 -6+14=8 -7+12=5$$

Ko te otinga te takirua ka hoatu i te tapeke 8.

$$a=14 b=-6$$

Tuhia anō te -7x^{2}+8x+12 hei \left(-7x^{2}+14x\right)+\left(-6x+12\right).

$$\left(-7x^{2}+14x\right)+\left(-6x+12\right)$$

Tauwehea te 7x i te tuatahi me te 6 i te rōpū tuarua.

$$7x\left(-x+2\right)+6\left(-x+2\right)$$

Whakatauwehea atu te kīanga pātahi -x+2 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(-x+2\right)\left(7x+6\right)$$

Hei kimi otinga whārite, me whakaoti te -x+2=0 me te 7x+6=0.

$$x=2 x=-\frac{6}{7}$$

Tē taea kia ōrite te tāupe x ki 2.

$$x=-\frac{6}{7}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -2,2 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te \left(x-2\right)\left(x+2\right), arā, te tauraro pātahi he tino iti rawa te kitea o x+2,x-2.

$$8x\left(x-2\right)\left(x+2\right)+\left(x-2\right)\left(x+2\right)\times 16+\left(x-2\right)\times 8\times \frac{1}{x-2}=\left(x+2\right)\left(8x^{2}-25\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 8x ki te x-2.

$$\left(8x^{2}-16x\right)\left(x+2\right)+\left(x-2\right)\left(x+2\right)\times 16+\left(x-2\right)\times 8\times \frac{1}{x-2}=\left(x+2\right)\left(8x^{2}-25\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 8x^{2}-16x ki te x+2 ka whakakotahi i ngā kupu rite.

$$8x^{3}-32x+\left(x-2\right)\left(x+2\right)\times 16+\left(x-2\right)\times 8\times \frac{1}{x-2}=\left(x+2\right)\left(8x^{2}-25\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x-2 ki te x+2 ka whakakotahi i ngā kupu rite.

$$8x^{3}-32x+\left(x^{2}-4\right)\times 16+\left(x-2\right)\times 8\times \frac{1}{x-2}=\left(x+2\right)\left(8x^{2}-25\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x^{2}-4 ki te 16.

$$8x^{3}-32x+16x^{2}-64+\left(x-2\right)\times 8\times \frac{1}{x-2}=\left(x+2\right)\left(8x^{2}-25\right)$$

Tuhia te \left(x-2\right)\times \frac{1}{x-2} hei hautanga kotahi.

$$8x^{3}-32x+16x^{2}-64+\frac{x-2}{x-2}\times 8=\left(x+2\right)\left(8x^{2}-25\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x+2 ki te 8x^{2}-25.

$$8x^{3}-32x+16x^{2}-64+\frac{x-2}{x-2}\times 8=8x^{3}-25x+16x^{2}-50$$

Tuhia te \frac{x-2}{x-2}\times 8 hei hautanga kotahi.

$$8x^{3}-32x+16x^{2}-64+\frac{\left(x-2\right)\times 8}{x-2}=8x^{3}-25x+16x^{2}-50$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 8x^{3}-32x+16x^{2}-64 ki te \frac{x-2}{x-2}.

$$\frac{\left(8x^{3}-32x+16x^{2}-64\right)\left(x-2\right)}{x-2}+\frac{\left(x-2\right)\times 8}{x-2}=8x^{3}-25x+16x^{2}-50$$

Tā te mea he rite te tauraro o \frac{\left(8x^{3}-32x+16x^{2}-64\right)\left(x-2\right)}{x-2} me \frac{\left(x-2\right)\times 8}{x-2}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\left(8x^{3}-32x+16x^{2}-64\right)\left(x-2\right)+\left(x-2\right)\times 8}{x-2}=8x^{3}-25x+16x^{2}-50$$

Mahia ngā whakarea i roto o \left(8x^{3}-32x+16x^{2}-64\right)\left(x-2\right)+\left(x-2\right)\times 8.

$$\frac{8x^{4}-16x^{3}-32x^{2}+64x+16x^{3}-32x^{2}-64x+128+8x-16}{x-2}=8x^{3}-25x+16x^{2}-50$$

Whakakotahitia ngā kupu rite i 8x^{4}-16x^{3}-32x^{2}+64x+16x^{3}-32x^{2}-64x+128+8x-16.

$$\frac{8x^{4}-64x^{2}+8x+112}{x-2}=8x^{3}-25x+16x^{2}-50$$

Tangohia te 8x^{3} mai i ngā taha e rua.

$$\frac{8x^{4}-64x^{2}+8x+112}{x-2}-8x^{3}=-25x+16x^{2}-50$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia -8x^{3} ki te \frac{x-2}{x-2}.

$$\frac{8x^{4}-64x^{2}+8x+112}{x-2}+\frac{-8x^{3}\left(x-2\right)}{x-2}=-25x+16x^{2}-50$$

Tā te mea he rite te tauraro o \frac{8x^{4}-64x^{2}+8x+112}{x-2} me \frac{-8x^{3}\left(x-2\right)}{x-2}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{8x^{4}-64x^{2}+8x+112-8x^{3}\left(x-2\right)}{x-2}=-25x+16x^{2}-50$$

Mahia ngā whakarea i roto o 8x^{4}-64x^{2}+8x+112-8x^{3}\left(x-2\right).

$$\frac{8x^{4}-64x^{2}+8x+112-8x^{4}+16x^{3}}{x-2}=-25x+16x^{2}-50$$

Whakakotahitia ngā kupu rite i 8x^{4}-64x^{2}+8x+112-8x^{4}+16x^{3}.

$$\frac{-64x^{2}+8x+112+16x^{3}}{x-2}=-25x+16x^{2}-50$$

Me tāpiri te 25x ki ngā taha e rua.

$$\frac{-64x^{2}+8x+112+16x^{3}}{x-2}+25x=16x^{2}-50$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 25x ki te \frac{x-2}{x-2}.

$$\frac{-64x^{2}+8x+112+16x^{3}}{x-2}+\frac{25x\left(x-2\right)}{x-2}=16x^{2}-50$$

Tā te mea he rite te tauraro o \frac{-64x^{2}+8x+112+16x^{3}}{x-2} me \frac{25x\left(x-2\right)}{x-2}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{-64x^{2}+8x+112+16x^{3}+25x\left(x-2\right)}{x-2}=16x^{2}-50$$

Mahia ngā whakarea i roto o -64x^{2}+8x+112+16x^{3}+25x\left(x-2\right).

$$\frac{-64x^{2}+8x+112+16x^{3}+25x^{2}-50x}{x-2}=16x^{2}-50$$

Whakakotahitia ngā kupu rite i -64x^{2}+8x+112+16x^{3}+25x^{2}-50x.

$$\frac{-39x^{2}-42x+112+16x^{3}}{x-2}=16x^{2}-50$$

Tangohia te 16x^{2} mai i ngā taha e rua.

$$\frac{-39x^{2}-42x+112+16x^{3}}{x-2}-16x^{2}=-50$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia -16x^{2} ki te \frac{x-2}{x-2}.

$$\frac{-39x^{2}-42x+112+16x^{3}}{x-2}+\frac{-16x^{2}\left(x-2\right)}{x-2}=-50$$

Tā te mea he rite te tauraro o \frac{-39x^{2}-42x+112+16x^{3}}{x-2} me \frac{-16x^{2}\left(x-2\right)}{x-2}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{-39x^{2}-42x+112+16x^{3}-16x^{2}\left(x-2\right)}{x-2}=-50$$

Mahia ngā whakarea i roto o -39x^{2}-42x+112+16x^{3}-16x^{2}\left(x-2\right).

$$\frac{-39x^{2}-42x+112+16x^{3}-16x^{3}+32x^{2}}{x-2}=-50$$

Whakakotahitia ngā kupu rite i -39x^{2}-42x+112+16x^{3}-16x^{3}+32x^{2}.

$$\frac{-7x^{2}-42x+112}{x-2}=-50$$

Me tāpiri te 50 ki ngā taha e rua.

$$\frac{-7x^{2}-42x+112}{x-2}+50=0$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 50 ki te \frac{x-2}{x-2}.

$$\frac{-7x^{2}-42x+112}{x-2}+\frac{50\left(x-2\right)}{x-2}=0$$

Tā te mea he rite te tauraro o \frac{-7x^{2}-42x+112}{x-2} me \frac{50\left(x-2\right)}{x-2}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{-7x^{2}-42x+112+50\left(x-2\right)}{x-2}=0$$

Mahia ngā whakarea i roto o -7x^{2}-42x+112+50\left(x-2\right).

$$\frac{-7x^{2}-42x+112+50x-100}{x-2}=0$$

Whakakotahitia ngā kupu rite i -7x^{2}-42x+112+50x-100.

$$\frac{-7x^{2}+8x+12}{x-2}=0$$

Tē taea kia ōrite te tāupe x ki 2 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x-2.

$$-7x^{2}+8x+12=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -7 mō a, 8 mō b, me 12 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-8±\sqrt{8^{2}-4\left(-7\right)\times 12}}{2\left(-7\right)}$$

Pūrua 8.

$$x=\frac{-8±\sqrt{64-4\left(-7\right)\times 12}}{2\left(-7\right)}$$

Whakareatia -4 ki te -7.

$$x=\frac{-8±\sqrt{64+28\times 12}}{2\left(-7\right)}$$

Whakareatia 28 ki te 12.

$$x=\frac{-8±\sqrt{64+336}}{2\left(-7\right)}$$

Tāpiri 64 ki te 336.

$$x=\frac{-8±\sqrt{400}}{2\left(-7\right)}$$

Tuhia te pūtakerua o te 400.

$$x=\frac{-8±20}{2\left(-7\right)}$$

Whakareatia 2 ki te -7.

$$x=\frac{-8±20}{-14}$$

Nā, me whakaoti te whārite x=\frac{-8±20}{-14} ina he tāpiri te ±. Tāpiri -8 ki te 20.

$$x=\frac{12}{-14}$$

Whakahekea te hautanga \frac{12}{-14} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=-\frac{6}{7}$$

Nā, me whakaoti te whārite x=\frac{-8±20}{-14} ina he tango te ±. Tango 20 mai i -8.

$$x=-\frac{28}{-14}$$

Whakawehe -28 ki te -14.

$$x=2$$

Kua oti te whārite te whakatau.

$$x=-\frac{6}{7} x=2$$

Tē taea kia ōrite te tāupe x ki 2.

$$x=-\frac{6}{7}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -2,2 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te \left(x-2\right)\left(x+2\right), arā, te tauraro pātahi he tino iti rawa te kitea o x+2,x-2.

$$8x\left(x-2\right)\left(x+2\right)+\left(x-2\right)\left(x+2\right)\times 16+\left(x-2\right)\times 8\times \frac{1}{x-2}=\left(x+2\right)\left(8x^{2}-25\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 8x ki te x-2.

$$\left(8x^{2}-16x\right)\left(x+2\right)+\left(x-2\right)\left(x+2\right)\times 16+\left(x-2\right)\times 8\times \frac{1}{x-2}=\left(x+2\right)\left(8x^{2}-25\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 8x^{2}-16x ki te x+2 ka whakakotahi i ngā kupu rite.

$$8x^{3}-32x+\left(x-2\right)\left(x+2\right)\times 16+\left(x-2\right)\times 8\times \frac{1}{x-2}=\left(x+2\right)\left(8x^{2}-25\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x-2 ki te x+2 ka whakakotahi i ngā kupu rite.

$$8x^{3}-32x+\left(x^{2}-4\right)\times 16+\left(x-2\right)\times 8\times \frac{1}{x-2}=\left(x+2\right)\left(8x^{2}-25\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x^{2}-4 ki te 16.

$$8x^{3}-32x+16x^{2}-64+\left(x-2\right)\times 8\times \frac{1}{x-2}=\left(x+2\right)\left(8x^{2}-25\right)$$

Tuhia te \left(x-2\right)\times \frac{1}{x-2} hei hautanga kotahi.

$$8x^{3}-32x+16x^{2}-64+\frac{x-2}{x-2}\times 8=\left(x+2\right)\left(8x^{2}-25\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x+2 ki te 8x^{2}-25.

$$8x^{3}-32x+16x^{2}-64+\frac{x-2}{x-2}\times 8=8x^{3}-25x+16x^{2}-50$$

Tuhia te \frac{x-2}{x-2}\times 8 hei hautanga kotahi.

$$8x^{3}-32x+16x^{2}-64+\frac{\left(x-2\right)\times 8}{x-2}=8x^{3}-25x+16x^{2}-50$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 8x^{3}-32x+16x^{2}-64 ki te \frac{x-2}{x-2}.

$$\frac{\left(8x^{3}-32x+16x^{2}-64\right)\left(x-2\right)}{x-2}+\frac{\left(x-2\right)\times 8}{x-2}=8x^{3}-25x+16x^{2}-50$$

Tā te mea he rite te tauraro o \frac{\left(8x^{3}-32x+16x^{2}-64\right)\left(x-2\right)}{x-2} me \frac{\left(x-2\right)\times 8}{x-2}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\left(8x^{3}-32x+16x^{2}-64\right)\left(x-2\right)+\left(x-2\right)\times 8}{x-2}=8x^{3}-25x+16x^{2}-50$$

Mahia ngā whakarea i roto o \left(8x^{3}-32x+16x^{2}-64\right)\left(x-2\right)+\left(x-2\right)\times 8.

$$\frac{8x^{4}-16x^{3}-32x^{2}+64x+16x^{3}-32x^{2}-64x+128+8x-16}{x-2}=8x^{3}-25x+16x^{2}-50$$

Whakakotahitia ngā kupu rite i 8x^{4}-16x^{3}-32x^{2}+64x+16x^{3}-32x^{2}-64x+128+8x-16.

$$\frac{8x^{4}-64x^{2}+8x+112}{x-2}=8x^{3}-25x+16x^{2}-50$$

Tangohia te 8x^{3} mai i ngā taha e rua.

$$\frac{8x^{4}-64x^{2}+8x+112}{x-2}-8x^{3}=-25x+16x^{2}-50$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia -8x^{3} ki te \frac{x-2}{x-2}.

$$\frac{8x^{4}-64x^{2}+8x+112}{x-2}+\frac{-8x^{3}\left(x-2\right)}{x-2}=-25x+16x^{2}-50$$

Tā te mea he rite te tauraro o \frac{8x^{4}-64x^{2}+8x+112}{x-2} me \frac{-8x^{3}\left(x-2\right)}{x-2}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{8x^{4}-64x^{2}+8x+112-8x^{3}\left(x-2\right)}{x-2}=-25x+16x^{2}-50$$

Mahia ngā whakarea i roto o 8x^{4}-64x^{2}+8x+112-8x^{3}\left(x-2\right).

$$\frac{8x^{4}-64x^{2}+8x+112-8x^{4}+16x^{3}}{x-2}=-25x+16x^{2}-50$$

Whakakotahitia ngā kupu rite i 8x^{4}-64x^{2}+8x+112-8x^{4}+16x^{3}.

$$\frac{-64x^{2}+8x+112+16x^{3}}{x-2}=-25x+16x^{2}-50$$

Me tāpiri te 25x ki ngā taha e rua.

$$\frac{-64x^{2}+8x+112+16x^{3}}{x-2}+25x=16x^{2}-50$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 25x ki te \frac{x-2}{x-2}.

$$\frac{-64x^{2}+8x+112+16x^{3}}{x-2}+\frac{25x\left(x-2\right)}{x-2}=16x^{2}-50$$

Tā te mea he rite te tauraro o \frac{-64x^{2}+8x+112+16x^{3}}{x-2} me \frac{25x\left(x-2\right)}{x-2}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{-64x^{2}+8x+112+16x^{3}+25x\left(x-2\right)}{x-2}=16x^{2}-50$$

Mahia ngā whakarea i roto o -64x^{2}+8x+112+16x^{3}+25x\left(x-2\right).

$$\frac{-64x^{2}+8x+112+16x^{3}+25x^{2}-50x}{x-2}=16x^{2}-50$$

Whakakotahitia ngā kupu rite i -64x^{2}+8x+112+16x^{3}+25x^{2}-50x.

$$\frac{-39x^{2}-42x+112+16x^{3}}{x-2}=16x^{2}-50$$

Tangohia te 16x^{2} mai i ngā taha e rua.

$$\frac{-39x^{2}-42x+112+16x^{3}}{x-2}-16x^{2}=-50$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia -16x^{2} ki te \frac{x-2}{x-2}.

$$\frac{-39x^{2}-42x+112+16x^{3}}{x-2}+\frac{-16x^{2}\left(x-2\right)}{x-2}=-50$$

Tā te mea he rite te tauraro o \frac{-39x^{2}-42x+112+16x^{3}}{x-2} me \frac{-16x^{2}\left(x-2\right)}{x-2}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{-39x^{2}-42x+112+16x^{3}-16x^{2}\left(x-2\right)}{x-2}=-50$$

Mahia ngā whakarea i roto o -39x^{2}-42x+112+16x^{3}-16x^{2}\left(x-2\right).

$$\frac{-39x^{2}-42x+112+16x^{3}-16x^{3}+32x^{2}}{x-2}=-50$$

Whakakotahitia ngā kupu rite i -39x^{2}-42x+112+16x^{3}-16x^{3}+32x^{2}.

$$\frac{-7x^{2}-42x+112}{x-2}=-50$$

Tē taea kia ōrite te tāupe x ki 2 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x-2.

$$-7x^{2}-42x+112=-50\left(x-2\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -50 ki te x-2.

$$-7x^{2}-42x+112=-50x+100$$

Me tāpiri te 50x ki ngā taha e rua.

$$-7x^{2}-42x+112+50x=100$$

Pahekotia te -42x me 50x, ka 8x.

$$-7x^{2}+8x+112=100$$

Tangohia te 112 mai i ngā taha e rua.

$$-7x^{2}+8x=100-112$$

Tangohia te 112 i te 100, ka -12.

$$-7x^{2}+8x=-12$$

Whakawehea ngā taha e rua ki te -7.

$$\frac{-7x^{2}+8x}{-7}=-\frac{12}{-7}$$

Mā te whakawehe ki te -7 ka wetekia te whakareanga ki te -7.

$$x^{2}+\frac{8}{-7}x=-\frac{12}{-7}$$

Whakawehe 8 ki te -7.

$$x^{2}-\frac{8}{7}x=-\frac{12}{-7}$$

Whakawehe -12 ki te -7.

$$x^{2}-\frac{8}{7}x=\frac{12}{7}$$

Whakawehea te -\frac{8}{7}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{4}{7}. Nā, tāpiria te pūrua o te -\frac{4}{7} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{8}{7}x+\left(-\frac{4}{7}\right)^{2}=\frac{12}{7}+\left(-\frac{4}{7}\right)^{2}$$

Pūruatia -\frac{4}{7} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{8}{7}x+\frac{16}{49}=\frac{12}{7}+\frac{16}{49}$$

Tāpiri \frac{12}{7} ki te \frac{16}{49} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x^{2}-\frac{8}{7}x+\frac{16}{49}=\frac{100}{49}$$

Tauwehea x^{2}-\frac{8}{7}x+\frac{16}{49}. Ko te tikanga pūnoa, ina ko x^{2}+bx+c he pūrua tika pūrua tika pū, ka taea taua mea te tauwehea i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{4}{7}\right)^{2}=\frac{100}{49}$$

Tuhia te pūtakerua o ngā taha e rua o te whārite.

$$\sqrt{\left(x-\frac{4}{7}\right)^{2}}=\sqrt{\frac{100}{49}}$$

Whakarūnātia.

$$x-\frac{4}{7}=\frac{10}{7} x-\frac{4}{7}=-\frac{10}{7}$$

Me tāpiri \frac{4}{7} ki ngā taha e rua o te whārite.

$$x=2 x=-\frac{6}{7}$$

Tē taea kia ōrite te tāupe x ki 2.

$$x=-\frac{6}{7}$$