Whakaoti i te x+z/x-z-x-z/x+z=z(2x^2+zy)/x^2-z^2

$$\frac{ x+z }{ x-z } - \frac{ x-z }{ x+z } = \frac{ z(2 { x }^{ 2 } +zy) }{ { x }^{ 2 } - { z }^{ 2 } }$$

Whakaoti mō y

$$\left\{\begin{matrix}y=-\frac{2x\left(x-2\right)}{z}\text{, }&z\neq 0\text{ and }|x|\neq |z|\\y\in \mathrm{R}\text{, }&z=0\text{ and }x\neq 0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te \left(x-z\right)\left(-x-z\right), arā, te tauraro pātahi he tino iti rawa te kitea o x-z,x+z,x^{2}-z^{2}.

$$\left(-x-z\right)\left(x+z\right)-\left(-x+z\right)\left(x-z\right)=-z\left(2x^{2}+zy\right)$$

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

$$-x^{2}-2xz-z^{2}-\left(-x+z\right)\left(x-z\right)=-z\left(2x^{2}+zy\right)$$

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

$$-x^{2}-2xz-z^{2}-\left(-x^{2}+2xz-z^{2}\right)=-z\left(2x^{2}+zy\right)$$

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

$$-x^{2}-2xz-z^{2}+x^{2}-2xz+z^{2}=-z\left(2x^{2}+zy\right)$$

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

$$-2xz-z^{2}-2xz+z^{2}=-z\left(2x^{2}+zy\right)$$

Pahekotia te -2xz me -2xz, ka -4xz.

$$-4xz-z^{2}+z^{2}=-z\left(2x^{2}+zy\right)$$

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

$$-4xz=-z\left(2x^{2}+zy\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te -z ki te 2x^{2}+zy.

$$-4xz=-2zx^{2}-yz^{2}$$

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

$$-2zx^{2}-yz^{2}=-4xz$$

Me tāpiri te 2zx^{2} ki ngā taha e rua.

$$-yz^{2}=-4xz+2zx^{2}$$

He hanga arowhānui tō te whārite.

$$\left(-z^{2}\right)y=2zx^{2}-4xz$$

Whakawehea ngā taha e rua ki te -z^{2}.

$$\frac{\left(-z^{2}\right)y}{-z^{2}}=\frac{2xz\left(x-2\right)}{-z^{2}}$$

Mā te whakawehe ki te -z^{2} ka wetekia te whakareanga ki te -z^{2}.

$$y=\frac{2xz\left(x-2\right)}{-z^{2}}$$

Whakawehe 2xz\left(-2+x\right) ki te -z^{2}.

$$y=-\frac{2x\left(x-2\right)}{z}$$