Whakaoti i te x+10/x=x-5/x+10

$$\frac { x + 10 } { x } = \frac { x - 5 } { x + 10 }$$

Whakaoti mō x

$$x=-4$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -10,0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te x\left(x+10\right), arā, te tauraro pātahi he tino iti rawa te kitea o x,x+10.

$$\left(x+10\right)\left(x+10\right)=x\left(x-5\right)$$

Whakareatia te x+10 ki te x+10, ka \left(x+10\right)^{2}.

$$\left(x+10\right)^{2}=x\left(x-5\right)$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(x+10\right)^{2}.

$$x^{2}+20x+100=x\left(x-5\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x-5.

$$x^{2}+20x+100=x^{2}-5x$$

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

$$x^{2}+20x+100-x^{2}=-5x$$

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

$$20x+100=-5x$$

Me tāpiri te 5x ki ngā taha e rua.

$$20x+100+5x=0$$

Pahekotia te 20x me 5x, ka 25x.

$$25x+100=0$$

Tangohia te 100 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$25x=-100$$

Whakawehea ngā taha e rua ki te 25.

$$x=\frac{-100}{25}$$

Whakawehea te -100 ki te 25, kia riro ko -4.

$$x=-4$$