Whakaoti i te x+1/x-5=x+9/x+7

$$\frac { x + 1 } { x - 5 } = \frac { x + 9 } { x + 7 }$$

Whakaoti mō x

$$x=-13$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -7,5 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+7\right), arā, te tauraro pātahi he tino iti rawa te kitea o x-5,x+7.

$$\left(x+7\right)\left(x+1\right)=\left(x-5\right)\left(x+9\right)$$

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

$$x^{2}+8x+7=\left(x-5\right)\left(x+9\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x-5 ki te x+9 ka whakakotahi i ngā kupu rite.

$$x^{2}+8x+7=x^{2}+4x-45$$

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

$$x^{2}+8x+7-x^{2}=4x-45$$

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

$$8x+7=4x-45$$

Tangohia te 4x mai i ngā taha e rua.

$$8x+7-4x=-45$$

Pahekotia te 8x me -4x, ka 4x.

$$4x+7=-45$$

Tangohia te 7 mai i ngā taha e rua.

$$4x=-45-7$$

Tangohia te 7 i te -45, ka -52.

$$4x=-52$$

Whakawehea ngā taha e rua ki te 4.

$$x=\frac{-52}{4}$$

Whakawehea te -52 ki te 4, kia riro ko -13.

$$x=-13$$