Whakaoti i te x^2-(x+5)(x-5)/x-5=3/7

$$\frac { x ^ { 2 } - ( x + 5 ) ( x - 5 ) } { x - 5 } = \frac { 3 } { 7 }$$

Whakaoti mō x

$$x = \frac{190}{3} = 63\frac{1}{3} \approx 63.333333333$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe x ki 5 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 7\left(x-5\right), arā, te tauraro pātahi he tino iti rawa te kitea o x-5,7.

$$7\left(x^{2}-\left(x+5\right)\left(x-5\right)\right)=3\left(x-5\right)$$

Whakaarohia te \left(x+5\right)\left(x-5\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Pūrua 5.

$$7\left(x^{2}-\left(x^{2}-25\right)\right)=3\left(x-5\right)$$

Hei kimi i te tauaro o x^{2}-25, kimihia te tauaro o ia taurangi.

$$7\left(x^{2}-x^{2}+25\right)=3\left(x-5\right)$$

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

$$7\times 25=3\left(x-5\right)$$

Whakareatia te 7 ki te 25, ka 175.

$$175=3\left(x-5\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te x-5.

$$175=3x-15$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$3x-15=175$$

Me tāpiri te 15 ki ngā taha e rua.

$$3x=175+15$$

Tāpirihia te 175 ki te 15, ka 190.

$$3x=190$$

Whakawehea ngā taha e rua ki te 3.

$$x=\frac{190}{3}$$