Whakaoti i te {l}{8x+16+8/x+2*7/x-2=8x^2-25/x-2}{8(x+2)+}

$$\left. \begin{array} { l } { 8 x + 16 + \frac { 8 } { x + 2 } \cdot \frac { 7 } { x - 2 } = \frac { 8 x ^ { 2 } - 25 } { x - 2 } } \\ { 8 ( x + 2 ) + } \end{array} \right.$$

Whakaoti mō x

$$x=6$$

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.

$$8x\left(x-2\right)\left(x+2\right)+\left(x-2\right)\left(x+2\right)\times 16+\left(x-2\right)\times 8\times \frac{7}{x-2}=\left(x+2\right)\left(8x^{2}-25\right)$$

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

$$\left(8x^{2}-16x\right)\left(x+2\right)+\left(x-2\right)\left(x+2\right)\times 16+\left(x-2\right)\times 8\times \frac{7}{x-2}=\left(x+2\right)\left(8x^{2}-25\right)$$

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

$$8x^{3}-32x+\left(x-2\right)\left(x+2\right)\times 16+\left(x-2\right)\times 8\times \frac{7}{x-2}=\left(x+2\right)\left(8x^{2}-25\right)$$

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

$$8x^{3}-32x+\left(x^{2}-4\right)\times 16+\left(x-2\right)\times 8\times \frac{7}{x-2}=\left(x+2\right)\left(8x^{2}-25\right)$$

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

$$8x^{3}-32x+16x^{2}-64+\left(x-2\right)\times 8\times \frac{7}{x-2}=\left(x+2\right)\left(8x^{2}-25\right)$$

Tuhia te \left(x-2\right)\times \frac{7}{x-2} hei hautanga kotahi.

$$8x^{3}-32x+16x^{2}-64+\frac{\left(x-2\right)\times 7}{x-2}\times 8=\left(x+2\right)\left(8x^{2}-25\right)$$

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

$$8x^{3}-32x+16x^{2}-64+\frac{\left(x-2\right)\times 7}{x-2}\times 8=8x^{3}-25x+16x^{2}-50$$

Whakamahia te āhuatanga tohatoha hei whakarea te x-2 ki te 7.

$$8x^{3}-32x+16x^{2}-64+\frac{7x-14}{x-2}\times 8=8x^{3}-25x+16x^{2}-50$$

Tuhia te \frac{7x-14}{x-2}\times 8 hei hautanga kotahi.

$$8x^{3}-32x+16x^{2}-64+\frac{\left(7x-14\right)\times 8}{x-2}=8x^{3}-25x+16x^{2}-50$$

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}.

$$\frac{\left(8x^{3}-32x+16x^{2}-64\right)\left(x-2\right)}{x-2}+\frac{\left(7x-14\right)\times 8}{x-2}=8x^{3}-25x+16x^{2}-50$$

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(7x-14\right)\times 8}{x-2}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\left(8x^{3}-32x+16x^{2}-64\right)\left(x-2\right)+\left(7x-14\right)\times 8}{x-2}=8x^{3}-25x+16x^{2}-50$$

Mahia ngā whakarea i roto o \left(8x^{3}-32x+16x^{2}-64\right)\left(x-2\right)+\left(7x-14\right)\times 8.

$$\frac{8x^{4}-16x^{3}-32x^{2}+64x+16x^{3}-32x^{2}-64x+128+56x-112}{x-2}=8x^{3}-25x+16x^{2}-50$$

Whakakotahitia ngā kupu rite i 8x^{4}-16x^{3}-32x^{2}+64x+16x^{3}-32x^{2}-64x+128+56x-112.

$$\frac{8x^{4}-64x^{2}+56x+16}{x-2}=8x^{3}-25x+16x^{2}-50$$

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

$$\frac{8x^{4}-64x^{2}+56x+16}{x-2}-8x^{3}=-25x+16x^{2}-50$$

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

$$\frac{8x^{4}-64x^{2}+56x+16}{x-2}+\frac{-8x^{3}\left(x-2\right)}{x-2}=-25x+16x^{2}-50$$

Tā te mea he rite te tauraro o \frac{8x^{4}-64x^{2}+56x+16}{x-2} me \frac{-8x^{3}\left(x-2\right)}{x-2}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{8x^{4}-64x^{2}+56x+16-8x^{3}\left(x-2\right)}{x-2}=-25x+16x^{2}-50$$

Mahia ngā whakarea i roto o 8x^{4}-64x^{2}+56x+16-8x^{3}\left(x-2\right).

$$\frac{8x^{4}-64x^{2}+56x+16-8x^{4}+16x^{3}}{x-2}=-25x+16x^{2}-50$$

Whakakotahitia ngā kupu rite i 8x^{4}-64x^{2}+56x+16-8x^{4}+16x^{3}.

$$\frac{-64x^{2}+56x+16+16x^{3}}{x-2}=-25x+16x^{2}-50$$

Me tāpiri te 25x ki ngā taha e rua.

$$\frac{-64x^{2}+56x+16+16x^{3}}{x-2}+25x=16x^{2}-50$$

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

$$\frac{-64x^{2}+56x+16+16x^{3}}{x-2}+\frac{25x\left(x-2\right)}{x-2}=16x^{2}-50$$

Tā te mea he rite te tauraro o \frac{-64x^{2}+56x+16+16x^{3}}{x-2} me \frac{25x\left(x-2\right)}{x-2}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{-64x^{2}+56x+16+16x^{3}+25x\left(x-2\right)}{x-2}=16x^{2}-50$$

Mahia ngā whakarea i roto o -64x^{2}+56x+16+16x^{3}+25x\left(x-2\right).

$$\frac{-64x^{2}+56x+16+16x^{3}+25x^{2}-50x}{x-2}=16x^{2}-50$$

Whakakotahitia ngā kupu rite i -64x^{2}+56x+16+16x^{3}+25x^{2}-50x.

$$\frac{-39x^{2}+6x+16+16x^{3}}{x-2}=16x^{2}-50$$

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

$$\frac{-39x^{2}+6x+16+16x^{3}}{x-2}-16x^{2}=-50$$

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

$$\frac{-39x^{2}+6x+16+16x^{3}}{x-2}+\frac{-16x^{2}\left(x-2\right)}{x-2}=-50$$

Tā te mea he rite te tauraro o \frac{-39x^{2}+6x+16+16x^{3}}{x-2} me \frac{-16x^{2}\left(x-2\right)}{x-2}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{-39x^{2}+6x+16+16x^{3}-16x^{2}\left(x-2\right)}{x-2}=-50$$

Mahia ngā whakarea i roto o -39x^{2}+6x+16+16x^{3}-16x^{2}\left(x-2\right).

$$\frac{-39x^{2}+6x+16+16x^{3}-16x^{3}+32x^{2}}{x-2}=-50$$

Whakakotahitia ngā kupu rite i -39x^{2}+6x+16+16x^{3}-16x^{3}+32x^{2}.

$$\frac{-7x^{2}+6x+16}{x-2}=-50$$

Me tāpiri te 50 ki ngā taha e rua.

$$\frac{-7x^{2}+6x+16}{x-2}+50=0$$

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

$$\frac{-7x^{2}+6x+16}{x-2}+\frac{50\left(x-2\right)}{x-2}=0$$

Tā te mea he rite te tauraro o \frac{-7x^{2}+6x+16}{x-2} me \frac{50\left(x-2\right)}{x-2}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{-7x^{2}+6x+16+50\left(x-2\right)}{x-2}=0$$

Mahia ngā whakarea i roto o -7x^{2}+6x+16+50\left(x-2\right).

$$\frac{-7x^{2}+6x+16+50x-100}{x-2}=0$$

Whakakotahitia ngā kupu rite i -7x^{2}+6x+16+50x-100.

$$\frac{-7x^{2}+56x-84}{x-2}=0$$

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.

$$-7x^{2}+56x-84=0$$

Whakawehea ngā taha e rua ki te 7.

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

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

$$a+b=8 ab=-\left(-12\right)=12$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōrunga te a+b, he tōrunga hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 12.

$$1,12 2,6 3,4$$

Tātaihia te tapeke mō ia takirua.

$$1+12=13 2+6=8 3+4=7$$

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

$$a=6 b=2$$

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

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

Tauwehea te -x i te tuatahi me te 2 i te rōpū tuarua.

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

Whakatauwehea atu te kīanga pātahi x-6 mā te whakamahi i te āhuatanga tātai tohatoha.

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

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

$$x=6 x=2$$

Tē taea kia ōrite te tāupe x ki 2.

$$x=6$$

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.

$$8x\left(x-2\right)\left(x+2\right)+\left(x-2\right)\left(x+2\right)\times 16+\left(x-2\right)\times 8\times \frac{7}{x-2}=\left(x+2\right)\left(8x^{2}-25\right)$$

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

$$\left(8x^{2}-16x\right)\left(x+2\right)+\left(x-2\right)\left(x+2\right)\times 16+\left(x-2\right)\times 8\times \frac{7}{x-2}=\left(x+2\right)\left(8x^{2}-25\right)$$

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

$$8x^{3}-32x+\left(x-2\right)\left(x+2\right)\times 16+\left(x-2\right)\times 8\times \frac{7}{x-2}=\left(x+2\right)\left(8x^{2}-25\right)$$

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

$$8x^{3}-32x+\left(x^{2}-4\right)\times 16+\left(x-2\right)\times 8\times \frac{7}{x-2}=\left(x+2\right)\left(8x^{2}-25\right)$$

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

$$8x^{3}-32x+16x^{2}-64+\left(x-2\right)\times 8\times \frac{7}{x-2}=\left(x+2\right)\left(8x^{2}-25\right)$$

Tuhia te \left(x-2\right)\times \frac{7}{x-2} hei hautanga kotahi.

$$8x^{3}-32x+16x^{2}-64+\frac{\left(x-2\right)\times 7}{x-2}\times 8=\left(x+2\right)\left(8x^{2}-25\right)$$

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

$$8x^{3}-32x+16x^{2}-64+\frac{\left(x-2\right)\times 7}{x-2}\times 8=8x^{3}-25x+16x^{2}-50$$

Whakamahia te āhuatanga tohatoha hei whakarea te x-2 ki te 7.

$$8x^{3}-32x+16x^{2}-64+\frac{7x-14}{x-2}\times 8=8x^{3}-25x+16x^{2}-50$$

Tuhia te \frac{7x-14}{x-2}\times 8 hei hautanga kotahi.

$$8x^{3}-32x+16x^{2}-64+\frac{\left(7x-14\right)\times 8}{x-2}=8x^{3}-25x+16x^{2}-50$$

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}.

$$\frac{\left(8x^{3}-32x+16x^{2}-64\right)\left(x-2\right)}{x-2}+\frac{\left(7x-14\right)\times 8}{x-2}=8x^{3}-25x+16x^{2}-50$$

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(7x-14\right)\times 8}{x-2}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\left(8x^{3}-32x+16x^{2}-64\right)\left(x-2\right)+\left(7x-14\right)\times 8}{x-2}=8x^{3}-25x+16x^{2}-50$$

Mahia ngā whakarea i roto o \left(8x^{3}-32x+16x^{2}-64\right)\left(x-2\right)+\left(7x-14\right)\times 8.

$$\frac{8x^{4}-16x^{3}-32x^{2}+64x+16x^{3}-32x^{2}-64x+128+56x-112}{x-2}=8x^{3}-25x+16x^{2}-50$$

Whakakotahitia ngā kupu rite i 8x^{4}-16x^{3}-32x^{2}+64x+16x^{3}-32x^{2}-64x+128+56x-112.

$$\frac{8x^{4}-64x^{2}+56x+16}{x-2}=8x^{3}-25x+16x^{2}-50$$

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

$$\frac{8x^{4}-64x^{2}+56x+16}{x-2}-8x^{3}=-25x+16x^{2}-50$$

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

$$\frac{8x^{4}-64x^{2}+56x+16}{x-2}+\frac{-8x^{3}\left(x-2\right)}{x-2}=-25x+16x^{2}-50$$

Tā te mea he rite te tauraro o \frac{8x^{4}-64x^{2}+56x+16}{x-2} me \frac{-8x^{3}\left(x-2\right)}{x-2}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{8x^{4}-64x^{2}+56x+16-8x^{3}\left(x-2\right)}{x-2}=-25x+16x^{2}-50$$

Mahia ngā whakarea i roto o 8x^{4}-64x^{2}+56x+16-8x^{3}\left(x-2\right).

$$\frac{8x^{4}-64x^{2}+56x+16-8x^{4}+16x^{3}}{x-2}=-25x+16x^{2}-50$$

Whakakotahitia ngā kupu rite i 8x^{4}-64x^{2}+56x+16-8x^{4}+16x^{3}.

$$\frac{-64x^{2}+56x+16+16x^{3}}{x-2}=-25x+16x^{2}-50$$

Me tāpiri te 25x ki ngā taha e rua.

$$\frac{-64x^{2}+56x+16+16x^{3}}{x-2}+25x=16x^{2}-50$$

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

$$\frac{-64x^{2}+56x+16+16x^{3}}{x-2}+\frac{25x\left(x-2\right)}{x-2}=16x^{2}-50$$

Tā te mea he rite te tauraro o \frac{-64x^{2}+56x+16+16x^{3}}{x-2} me \frac{25x\left(x-2\right)}{x-2}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{-64x^{2}+56x+16+16x^{3}+25x\left(x-2\right)}{x-2}=16x^{2}-50$$

Mahia ngā whakarea i roto o -64x^{2}+56x+16+16x^{3}+25x\left(x-2\right).

$$\frac{-64x^{2}+56x+16+16x^{3}+25x^{2}-50x}{x-2}=16x^{2}-50$$

Whakakotahitia ngā kupu rite i -64x^{2}+56x+16+16x^{3}+25x^{2}-50x.

$$\frac{-39x^{2}+6x+16+16x^{3}}{x-2}=16x^{2}-50$$

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

$$\frac{-39x^{2}+6x+16+16x^{3}}{x-2}-16x^{2}=-50$$

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

$$\frac{-39x^{2}+6x+16+16x^{3}}{x-2}+\frac{-16x^{2}\left(x-2\right)}{x-2}=-50$$

Tā te mea he rite te tauraro o \frac{-39x^{2}+6x+16+16x^{3}}{x-2} me \frac{-16x^{2}\left(x-2\right)}{x-2}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{-39x^{2}+6x+16+16x^{3}-16x^{2}\left(x-2\right)}{x-2}=-50$$

Mahia ngā whakarea i roto o -39x^{2}+6x+16+16x^{3}-16x^{2}\left(x-2\right).

$$\frac{-39x^{2}+6x+16+16x^{3}-16x^{3}+32x^{2}}{x-2}=-50$$

Whakakotahitia ngā kupu rite i -39x^{2}+6x+16+16x^{3}-16x^{3}+32x^{2}.

$$\frac{-7x^{2}+6x+16}{x-2}=-50$$

Me tāpiri te 50 ki ngā taha e rua.

$$\frac{-7x^{2}+6x+16}{x-2}+50=0$$

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

$$\frac{-7x^{2}+6x+16}{x-2}+\frac{50\left(x-2\right)}{x-2}=0$$

Tā te mea he rite te tauraro o \frac{-7x^{2}+6x+16}{x-2} me \frac{50\left(x-2\right)}{x-2}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{-7x^{2}+6x+16+50\left(x-2\right)}{x-2}=0$$

Mahia ngā whakarea i roto o -7x^{2}+6x+16+50\left(x-2\right).

$$\frac{-7x^{2}+6x+16+50x-100}{x-2}=0$$

Whakakotahitia ngā kupu rite i -7x^{2}+6x+16+50x-100.

$$\frac{-7x^{2}+56x-84}{x-2}=0$$

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.

$$-7x^{2}+56x-84=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -7 mō a, 56 mō b, me -84 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-56±\sqrt{56^{2}-4\left(-7\right)\left(-84\right)}}{2\left(-7\right)}$$

Pūrua 56.

$$x=\frac{-56±\sqrt{3136-4\left(-7\right)\left(-84\right)}}{2\left(-7\right)}$$

Whakareatia -4 ki te -7.

$$x=\frac{-56±\sqrt{3136+28\left(-84\right)}}{2\left(-7\right)}$$

Whakareatia 28 ki te -84.

$$x=\frac{-56±\sqrt{3136-2352}}{2\left(-7\right)}$$

Tāpiri 3136 ki te -2352.

$$x=\frac{-56±\sqrt{784}}{2\left(-7\right)}$$

Tuhia te pūtakerua o te 784.

$$x=\frac{-56±28}{2\left(-7\right)}$$

Whakareatia 2 ki te -7.

$$x=\frac{-56±28}{-14}$$

Nā, me whakaoti te whārite x=\frac{-56±28}{-14} ina he tāpiri te ±. Tāpiri -56 ki te 28.

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

Whakawehe -28 ki te -14.

$$x=2$$

Nā, me whakaoti te whārite x=\frac{-56±28}{-14} ina he tango te ±. Tango 28 mai i -56.

$$x=-\frac{84}{-14}$$

Whakawehe -84 ki te -14.

$$x=6$$

Kua oti te whārite te whakatau.

$$x=2 x=6$$

Tē taea kia ōrite te tāupe x ki 2.

$$x=6$$

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.

$$8x\left(x-2\right)\left(x+2\right)+\left(x-2\right)\left(x+2\right)\times 16+\left(x-2\right)\times 8\times \frac{7}{x-2}=\left(x+2\right)\left(8x^{2}-25\right)$$

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

$$\left(8x^{2}-16x\right)\left(x+2\right)+\left(x-2\right)\left(x+2\right)\times 16+\left(x-2\right)\times 8\times \frac{7}{x-2}=\left(x+2\right)\left(8x^{2}-25\right)$$

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

$$8x^{3}-32x+\left(x-2\right)\left(x+2\right)\times 16+\left(x-2\right)\times 8\times \frac{7}{x-2}=\left(x+2\right)\left(8x^{2}-25\right)$$

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

$$8x^{3}-32x+\left(x^{2}-4\right)\times 16+\left(x-2\right)\times 8\times \frac{7}{x-2}=\left(x+2\right)\left(8x^{2}-25\right)$$

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

$$8x^{3}-32x+16x^{2}-64+\left(x-2\right)\times 8\times \frac{7}{x-2}=\left(x+2\right)\left(8x^{2}-25\right)$$

Tuhia te \left(x-2\right)\times \frac{7}{x-2} hei hautanga kotahi.

$$8x^{3}-32x+16x^{2}-64+\frac{\left(x-2\right)\times 7}{x-2}\times 8=\left(x+2\right)\left(8x^{2}-25\right)$$

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

$$8x^{3}-32x+16x^{2}-64+\frac{\left(x-2\right)\times 7}{x-2}\times 8=8x^{3}-25x+16x^{2}-50$$

Whakamahia te āhuatanga tohatoha hei whakarea te x-2 ki te 7.

$$8x^{3}-32x+16x^{2}-64+\frac{7x-14}{x-2}\times 8=8x^{3}-25x+16x^{2}-50$$

Tuhia te \frac{7x-14}{x-2}\times 8 hei hautanga kotahi.

$$8x^{3}-32x+16x^{2}-64+\frac{\left(7x-14\right)\times 8}{x-2}=8x^{3}-25x+16x^{2}-50$$

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}.

$$\frac{\left(8x^{3}-32x+16x^{2}-64\right)\left(x-2\right)}{x-2}+\frac{\left(7x-14\right)\times 8}{x-2}=8x^{3}-25x+16x^{2}-50$$

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(7x-14\right)\times 8}{x-2}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\left(8x^{3}-32x+16x^{2}-64\right)\left(x-2\right)+\left(7x-14\right)\times 8}{x-2}=8x^{3}-25x+16x^{2}-50$$

Mahia ngā whakarea i roto o \left(8x^{3}-32x+16x^{2}-64\right)\left(x-2\right)+\left(7x-14\right)\times 8.

$$\frac{8x^{4}-16x^{3}-32x^{2}+64x+16x^{3}-32x^{2}-64x+128+56x-112}{x-2}=8x^{3}-25x+16x^{2}-50$$

Whakakotahitia ngā kupu rite i 8x^{4}-16x^{3}-32x^{2}+64x+16x^{3}-32x^{2}-64x+128+56x-112.

$$\frac{8x^{4}-64x^{2}+56x+16}{x-2}=8x^{3}-25x+16x^{2}-50$$

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

$$\frac{8x^{4}-64x^{2}+56x+16}{x-2}-8x^{3}=-25x+16x^{2}-50$$

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

$$\frac{8x^{4}-64x^{2}+56x+16}{x-2}+\frac{-8x^{3}\left(x-2\right)}{x-2}=-25x+16x^{2}-50$$

Tā te mea he rite te tauraro o \frac{8x^{4}-64x^{2}+56x+16}{x-2} me \frac{-8x^{3}\left(x-2\right)}{x-2}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{8x^{4}-64x^{2}+56x+16-8x^{3}\left(x-2\right)}{x-2}=-25x+16x^{2}-50$$

Mahia ngā whakarea i roto o 8x^{4}-64x^{2}+56x+16-8x^{3}\left(x-2\right).

$$\frac{8x^{4}-64x^{2}+56x+16-8x^{4}+16x^{3}}{x-2}=-25x+16x^{2}-50$$

Whakakotahitia ngā kupu rite i 8x^{4}-64x^{2}+56x+16-8x^{4}+16x^{3}.

$$\frac{-64x^{2}+56x+16+16x^{3}}{x-2}=-25x+16x^{2}-50$$

Me tāpiri te 25x ki ngā taha e rua.

$$\frac{-64x^{2}+56x+16+16x^{3}}{x-2}+25x=16x^{2}-50$$

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

$$\frac{-64x^{2}+56x+16+16x^{3}}{x-2}+\frac{25x\left(x-2\right)}{x-2}=16x^{2}-50$$

Tā te mea he rite te tauraro o \frac{-64x^{2}+56x+16+16x^{3}}{x-2} me \frac{25x\left(x-2\right)}{x-2}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{-64x^{2}+56x+16+16x^{3}+25x\left(x-2\right)}{x-2}=16x^{2}-50$$

Mahia ngā whakarea i roto o -64x^{2}+56x+16+16x^{3}+25x\left(x-2\right).

$$\frac{-64x^{2}+56x+16+16x^{3}+25x^{2}-50x}{x-2}=16x^{2}-50$$

Whakakotahitia ngā kupu rite i -64x^{2}+56x+16+16x^{3}+25x^{2}-50x.

$$\frac{-39x^{2}+6x+16+16x^{3}}{x-2}=16x^{2}-50$$

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

$$\frac{-39x^{2}+6x+16+16x^{3}}{x-2}-16x^{2}=-50$$

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

$$\frac{-39x^{2}+6x+16+16x^{3}}{x-2}+\frac{-16x^{2}\left(x-2\right)}{x-2}=-50$$

Tā te mea he rite te tauraro o \frac{-39x^{2}+6x+16+16x^{3}}{x-2} me \frac{-16x^{2}\left(x-2\right)}{x-2}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{-39x^{2}+6x+16+16x^{3}-16x^{2}\left(x-2\right)}{x-2}=-50$$

Mahia ngā whakarea i roto o -39x^{2}+6x+16+16x^{3}-16x^{2}\left(x-2\right).

$$\frac{-39x^{2}+6x+16+16x^{3}-16x^{3}+32x^{2}}{x-2}=-50$$

Whakakotahitia ngā kupu rite i -39x^{2}+6x+16+16x^{3}-16x^{3}+32x^{2}.

$$\frac{-7x^{2}+6x+16}{x-2}=-50$$

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.

$$-7x^{2}+6x+16=-50\left(x-2\right)$$

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

$$-7x^{2}+6x+16=-50x+100$$

Me tāpiri te 50x ki ngā taha e rua.

$$-7x^{2}+6x+16+50x=100$$

Pahekotia te 6x me 50x, ka 56x.

$$-7x^{2}+56x+16=100$$

Tangohia te 16 mai i ngā taha e rua.

$$-7x^{2}+56x=100-16$$

Tangohia te 16 i te 100, ka 84.

$$-7x^{2}+56x=84$$

Whakawehea ngā taha e rua ki te -7.

$$\frac{-7x^{2}+56x}{-7}=\frac{84}{-7}$$

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

$$x^{2}+\frac{56}{-7}x=\frac{84}{-7}$$

Whakawehe 56 ki te -7.

$$x^{2}-8x=\frac{84}{-7}$$

Whakawehe 84 ki te -7.

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

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

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

Pūrua -4.

$$x^{2}-8x+16=-12+16$$

Tāpiri -12 ki te 16.

$$x^{2}-8x+16=4$$

Tauwehea x^{2}-8x+16. 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}.

$$\left(x-4\right)^{2}=4$$

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

$$\sqrt{\left(x-4\right)^{2}}=\sqrt{4}$$

Whakarūnātia.

$$x-4=2 x-4=-2$$

Me tāpiri 4 ki ngā taha e rua o te whārite.

$$x=6 x=2$$

Tē taea kia ōrite te tāupe x ki 2.

$$x=6$$