Solve xleft(x+1right)/left(2-xright)left(2+xright)=y

$$\frac{ x \left( x+1 \right) }{ \left( 2-x \right) \left( 2+x \right) } = y$$

Solve for y

$$y=-\frac{x\left(x+1\right)}{x^{2}-4}$$

$$|x|\neq 2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \left(x-2\right)\left(-x-2\right).

$$x\left(x+1\right)=y\left(x-2\right)\left(-x-2\right)$$

Use the distributive property to multiply x by x+1.

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

Use the distributive property to multiply y by x-2.

$$x^{2}+x=\left(yx-2y\right)\left(-x-2\right)$$

Use the distributive property to multiply yx-2y by -x-2 and combine like terms.

$$x^{2}+x=-yx^{2}+4y$$

Swap sides so that all variable terms are on the left hand side.

$$-yx^{2}+4y=x^{2}+x$$

Combine all terms containing y.

$$\left(-x^{2}+4\right)y=x^{2}+x$$

The equation is in standard form.

$$\left(4-x^{2}\right)y=x^{2}+x$$

Divide both sides by -x^{2}+4.

$$\frac{\left(4-x^{2}\right)y}{4-x^{2}}=\frac{x\left(x+1\right)}{4-x^{2}}$$

Dividing by -x^{2}+4 undoes the multiplication by -x^{2}+4.

$$y=\frac{x\left(x+1\right)}{4-x^{2}}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{16y^{2}+16y+1}-1}{2\left(y+1\right)}\text{; }x=-\frac{\sqrt{16y^{2}+16y+1}+1}{2\left(y+1\right)}\text{, }&\left(y\neq -1\text{ and }y\leq -\frac{\sqrt{3}}{4}-\frac{1}{2}\right)\text{ or }y\geq \frac{\sqrt{3}}{4}-\frac{1}{2}\\x=-4\text{, }&y=-1\end{matrix}\right.$$