Solve y^2-x/1-xy=a

$$\frac { y ^ { 2 } - x } { 1 - x y } = a$$

Solve for a

$$a=-\frac{y^{2}-x}{xy-1}$$

$$x=0\text{ or }y\neq \frac{1}{x}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by -xy+1.

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

Use the distributive property to multiply a by -xy+1.

$$y^{2}-x=-axy+a$$

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

$$-axy+a=y^{2}-x$$

Combine all terms containing a.

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

The equation is in standard form.

$$\left(1-xy\right)a=y^{2}-x$$

Divide both sides by 1-xy.

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

Dividing by 1-xy undoes the multiplication by 1-xy.

$$a=\frac{y^{2}-x}{1-xy}$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{y^{2}-a}{ay-1}\text{, }&\left(y\neq 1\text{ and }a=0\text{ and }y\neq 0\right)\text{ or }\left(y\neq 1\text{ and }y\neq 0\text{ and }y\neq \frac{1}{a}\text{ and }|y|\neq \sqrt{a}\text{ and }a>0\right)\text{ or }\left(y\neq 1\text{ and }y\neq 0\text{ and }a=y^{2}\right)\text{ or }\left(y\neq 1\text{ and }y\neq 0\text{ and }y\neq \frac{1}{a}\text{ and }a<0\right)\text{ or }\left(y\neq 0\text{ and }a=1\text{ and }y\neq 1\right)\text{ or }y=0\\x\neq 1\text{, }&y=1\text{ and }a=1\end{matrix}\right.$$