Whakaoti i te x+6/x-5+x-5/x+6=2x^2+23x+61/x^2+x-30

$$\frac{ x+6 }{ x-5 } + \frac{ x-5 }{ x+6 } = \frac{ 2 { x }^{ 2 } +23x+61 }{ { x }^{ 2 } +x-30 }$$

Whakaoti mō x

$$x=0$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -6,5 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te \left(x-5\right)\left(x+6\right), arā, te tauraro pātahi he tino iti rawa te kitea o x-5,x+6,x^{2}+x-30.

$$\left(x+6\right)\left(x+6\right)+\left(x-5\right)\left(x-5\right)=2x^{2}+23x+61$$

Whakareatia te x+6 ki te x+6, ka \left(x+6\right)^{2}.

$$\left(x+6\right)^{2}+\left(x-5\right)\left(x-5\right)=2x^{2}+23x+61$$

Whakareatia te x-5 ki te x-5, ka \left(x-5\right)^{2}.

$$\left(x+6\right)^{2}+\left(x-5\right)^{2}=2x^{2}+23x+61$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(x+6\right)^{2}.

$$x^{2}+12x+36+\left(x-5\right)^{2}=2x^{2}+23x+61$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-5\right)^{2}.

$$x^{2}+12x+36+x^{2}-10x+25=2x^{2}+23x+61$$

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

$$2x^{2}+12x+36-10x+25=2x^{2}+23x+61$$

Pahekotia te 12x me -10x, ka 2x.

$$2x^{2}+2x+36+25=2x^{2}+23x+61$$

Tāpirihia te 36 ki te 25, ka 61.

$$2x^{2}+2x+61=2x^{2}+23x+61$$

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

$$2x^{2}+2x+61-2x^{2}=23x+61$$

Pahekotia te 2x^{2} me -2x^{2}, ka 0.

$$2x+61=23x+61$$

Tangohia te 23x mai i ngā taha e rua.

$$2x+61-23x=61$$

Pahekotia te 2x me -23x, ka -21x.

$$-21x+61=61$$

Tangohia te 61 mai i ngā taha e rua.

$$-21x=61-61$$

Tangohia te 61 i te 61, ka 0.

$$-21x=0$$

He ōrite te hua o ngā tau e rua ki 0 ina 0 tētahi o rāua te iti rawa. Tātemea kāore te -21 e ōrite ki 0, me ōrite pū te x ki 0.

$$x=0$$