Whakaoti i te 2x-7/x-4-x+2/x+1=x+6/(x-4)(x+1)

$$\frac { 2 x - 7 } { x - 4 } - \frac { x + 2 } { x + 1 } = \frac { x + 6 } { ( x - 4 ) ( x + 1 ) }$$

Whakaoti mō x

$$x=5$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -1,4 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te \left(x-4\right)\left(x+1\right), arā, te tauraro pātahi he tino iti rawa te kitea o x-4,x+1,\left(x-4\right)\left(x+1\right).

$$\left(x+1\right)\left(2x-7\right)-\left(x-4\right)\left(x+2\right)=x+6$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x+1 ki te 2x-7 ka whakakotahi i ngā kupu rite.

$$2x^{2}-5x-7-\left(x-4\right)\left(x+2\right)=x+6$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x-4 ki te x+2 ka whakakotahi i ngā kupu rite.

$$2x^{2}-5x-7-\left(x^{2}-2x-8\right)=x+6$$

Hei kimi i te tauaro o x^{2}-2x-8, kimihia te tauaro o ia taurangi.

$$2x^{2}-5x-7-x^{2}+2x+8=x+6$$

Pahekotia te 2x^{2} me -x^{2}, ka x^{2}.

$$x^{2}-5x-7+2x+8=x+6$$

Pahekotia te -5x me 2x, ka -3x.

$$x^{2}-3x-7+8=x+6$$

Tāpirihia te -7 ki te 8, ka 1.

$$x^{2}-3x+1=x+6$$

Tangohia te x mai i ngā taha e rua.

$$x^{2}-3x+1-x=6$$

Pahekotia te -3x me -x, ka -4x.

$$x^{2}-4x+1=6$$

Tangohia te 6 mai i ngā taha e rua.

$$x^{2}-4x+1-6=0$$

Tangohia te 6 i te 1, ka -5.

$$x^{2}-4x-5=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -4 mō b, me -5 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\left(-5\right)}}{2}$$

Pūrua -4.

$$x=\frac{-\left(-4\right)±\sqrt{16-4\left(-5\right)}}{2}$$

Whakareatia -4 ki te -5.

$$x=\frac{-\left(-4\right)±\sqrt{16+20}}{2}$$

Tāpiri 16 ki te 20.

$$x=\frac{-\left(-4\right)±\sqrt{36}}{2}$$

Tuhia te pūtakerua o te 36.

$$x=\frac{-\left(-4\right)±6}{2}$$

Ko te tauaro o -4 ko 4.

$$x=\frac{4±6}{2}$$

Nā, me whakaoti te whārite x=\frac{4±6}{2} ina he tāpiri te ±. Tāpiri 4 ki te 6.

$$x=\frac{10}{2}$$

Whakawehe 10 ki te 2.

$$x=5$$

Nā, me whakaoti te whārite x=\frac{4±6}{2} ina he tango te ±. Tango 6 mai i 4.

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

Whakawehe -2 ki te 2.

$$x=-1$$

Kua oti te whārite te whakatau.

$$x=5 x=-1$$

Tē taea kia ōrite te tāupe x ki -1.

$$x=5$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -1,4 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te \left(x-4\right)\left(x+1\right), arā, te tauraro pātahi he tino iti rawa te kitea o x-4,x+1,\left(x-4\right)\left(x+1\right).

$$\left(x+1\right)\left(2x-7\right)-\left(x-4\right)\left(x+2\right)=x+6$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x+1 ki te 2x-7 ka whakakotahi i ngā kupu rite.

$$2x^{2}-5x-7-\left(x-4\right)\left(x+2\right)=x+6$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x-4 ki te x+2 ka whakakotahi i ngā kupu rite.

$$2x^{2}-5x-7-\left(x^{2}-2x-8\right)=x+6$$

Hei kimi i te tauaro o x^{2}-2x-8, kimihia te tauaro o ia taurangi.

$$2x^{2}-5x-7-x^{2}+2x+8=x+6$$

Pahekotia te 2x^{2} me -x^{2}, ka x^{2}.

$$x^{2}-5x-7+2x+8=x+6$$

Pahekotia te -5x me 2x, ka -3x.

$$x^{2}-3x-7+8=x+6$$

Tāpirihia te -7 ki te 8, ka 1.

$$x^{2}-3x+1=x+6$$

Tangohia te x mai i ngā taha e rua.

$$x^{2}-3x+1-x=6$$

Pahekotia te -3x me -x, ka -4x.

$$x^{2}-4x+1=6$$

Tangohia te 1 mai i ngā taha e rua.

$$x^{2}-4x=6-1$$

Tangohia te 1 i te 6, ka 5.

$$x^{2}-4x=5$$

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

$$x^{2}-4x+\left(-2\right)^{2}=5+\left(-2\right)^{2}$$

Pūrua -2.

$$x^{2}-4x+4=5+4$$

Tāpiri 5 ki te 4.

$$x^{2}-4x+4=9$$

Tauwehea te x^{2}-4x+4. Ko te tikanga, ina ko x^{2}+bx+c he pūrua tika, ka taea te tauwehe i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-2\right)^{2}=9$$

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

$$\sqrt{\left(x-2\right)^{2}}=\sqrt{9}$$

Whakarūnātia.

$$x-2=3 x-2=-3$$

Me tāpiri 2 ki ngā taha e rua o te whārite.

$$x=5 x=-1$$

Tē taea kia ōrite te tāupe x ki -1.

$$x=5$$