Issolvi x+z/x-z-x-z/x+z=z(2x^2+zy)/x^2-z^2

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

Solvi għal y (complex solution)

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

Passi biex Issolvi l-Ekwazzjoni Lineari

Immultiplika ż-żewġ naħat tal-ekwazzjoni b'\left(x-z\right)\left(-x-z\right), l-inqas denominatur komuni ta' x-z,x+z,x^{2}-z^{2}.

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

Uża l-propjetà distributtiva biex timmultiplika -x-z b'x+z u kkombina termini simili.

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

Uża l-propjetà distributtiva biex timmultiplika -x+z b'x-z u kkombina termini simili.

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

Biex issib l-oppost ta' -x^{2}+2xz-z^{2}, sib l-oppost ta' kull terminu.

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

Ikkombina -x^{2} u x^{2} biex tikseb 0.

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

Ikkombina -2xz u -2xz biex tikseb -4xz.

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

Ikkombina -z^{2} u z^{2} biex tikseb 0.

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

Uża l-propjetà distributtiva biex timmultiplika -z b'2x^{2}+zy.

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

Ibdel in-naħat sabiex it-termini varjabbli kollha jkunu fuq in-naħa tax-xellug.

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

Żid 2zx^{2} maż-żewġ naħat.

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

L-ekwazzjoni hija f'forma standard.

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

Iddividi ż-żewġ naħat b'-z^{2}.

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

Meta tiddividi b'-z^{2} titneħħa l-multiplikazzjoni b'-z^{2}.

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

Iddividi 2xz\left(-2+x\right) b'-z^{2}.

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

Solvi għal y

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

Passi biex Issolvi l-Ekwazzjoni Lineari

Immultiplika ż-żewġ naħat tal-ekwazzjoni b'\left(x-z\right)\left(-x-z\right), l-inqas denominatur komuni ta' x-z,x+z,x^{2}-z^{2}.

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

Uża l-propjetà distributtiva biex timmultiplika -x-z b'x+z u kkombina termini simili.

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

Uża l-propjetà distributtiva biex timmultiplika -x+z b'x-z u kkombina termini simili.

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

Biex issib l-oppost ta' -x^{2}+2xz-z^{2}, sib l-oppost ta' kull terminu.

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

Ikkombina -x^{2} u x^{2} biex tikseb 0.

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

Ikkombina -2xz u -2xz biex tikseb -4xz.

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

Ikkombina -z^{2} u z^{2} biex tikseb 0.

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

Uża l-propjetà distributtiva biex timmultiplika -z b'2x^{2}+zy.

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

Ibdel in-naħat sabiex it-termini varjabbli kollha jkunu fuq in-naħa tax-xellug.

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

Żid 2zx^{2} maż-żewġ naħat.

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

L-ekwazzjoni hija f'forma standard.

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

Iddividi ż-żewġ naħat b'-z^{2}.

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

Meta tiddividi b'-z^{2} titneħħa l-multiplikazzjoni b'-z^{2}.

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

Iddividi 2xz\left(-2+x\right) b'-z^{2}.

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

Solvi għal x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{4-2yz}}{2}+1\text{, }&\left(z\neq -\frac{y}{2}+2\text{ and }z\neq -\frac{y}{2}-2\right)\text{ or }\left(z\neq -\frac{y}{2}+2\text{ and }y\neq -2\text{ and }arg(-\frac{y}{2}-1)<\pi \right)\text{ or }\left(arg(2-y)\geq \pi \text{ and }y\neq 2\text{ and }z\neq -\frac{y}{2}-2\right)\text{ or }\left(arg(2-y)\geq \pi \text{ and }y\neq 2\text{ and }arg(-\frac{y}{2}-1)<\pi \right)\\x=-\frac{\sqrt{4-2yz}}{2}+1\text{, }&\left(z\neq 0\text{ and }z\neq -\frac{y}{2}+2\text{ and }arg(-\frac{y}{2}-1)\geq \pi \text{ and }z\neq -1\right)\text{ or }\left(z\neq 0\text{ and }z\neq -\frac{y}{2}+2\text{ and }arg(-\frac{y}{2}-1)\geq \pi \text{ and }y\neq -2\right)\text{ or }\left(z\neq 0\text{ and }z\neq -\frac{y}{2}+2\text{ and }z\neq -\frac{y}{2}-2\text{ and }z\neq -1\right)\text{ or }\left(z\neq 0\text{ and }z\neq -\frac{y}{2}+2\text{ and }z\neq -\frac{y}{2}-2\text{ and }y\neq -2\right)\text{ or }\left(z\neq 0\text{ and }z\neq 1\text{ and }arg(y-2)\geq \pi \text{ and }arg(-\frac{y}{2}-1)\geq \pi \text{ and }z\neq -1\right)\text{ or }\left(z\neq 0\text{ and }z\neq 1\text{ and }arg(y-2)\geq \pi \text{ and }arg(-\frac{y}{2}-1)\geq \pi \text{ and }y\neq -2\right)\text{ or }\left(z\neq 0\text{ and }z\neq 1\text{ and }arg(y-2)\geq \pi \text{ and }z\neq -\frac{y}{2}-2\text{ and }z\neq -1\right)\text{ or }\left(z\neq 0\text{ and }z\neq 1\text{ and }arg(y-2)\geq \pi \text{ and }z\neq -\frac{y}{2}-2\text{ and }y\neq -2\right)\text{ or }\left(z\neq 0\text{ and }y\neq 2\text{ and }arg(y-2)\geq \pi \text{ and }arg(-\frac{y}{2}-1)\geq \pi \text{ and }z\neq -1\right)\text{ or }\left(z\neq 0\text{ and }y\neq 2\text{ and }arg(y-2)\geq \pi \text{ and }arg(-\frac{y}{2}-1)\geq \pi \text{ and }y\neq -2\right)\text{ or }\left(z\neq 0\text{ and }y\neq 2\text{ and }arg(y-2)\geq \pi \text{ and }z\neq -\frac{y}{2}-2\text{ and }z\neq -1\right)\text{ or }\left(z\neq 0\text{ and }y\neq 2\text{ and }arg(y-2)\geq \pi \text{ and }z\neq -\frac{y}{2}-2\text{ and }y\neq -2\right)\\x\neq 0\text{, }&z=0\end{matrix}\right.$$