Solve (x-y)(x-z)=1+x^2

$$( x - y ) ( x - z ) = 1 + x ^ { 2 }$$

Solve for x

$$x=\frac{yz-1}{y+z}$$

$$y\neq -z$$

Steps for Solving Linear Equation

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

$$x^{2}-xz-yx+yz=1+x^{2}$$

Subtract x^{2} from both sides.

$$x^{2}-xz-yx+yz-x^{2}=1$$

Combine x^{2} and -x^{2} to get 0.

$$-xz-yx+yz=1$$

Subtract yz from both sides.

$$-xz-yx=1-yz$$

Combine all terms containing x.

$$\left(-z-y\right)x=1-yz$$

The equation is in standard form.

$$\left(-y-z\right)x=1-yz$$

Divide both sides by -y-z.

$$\frac{\left(-y-z\right)x}{-y-z}=\frac{1-yz}{-y-z}$$

Dividing by -y-z undoes the multiplication by -y-z.

$$x=\frac{1-yz}{-y-z}$$

Divide 1-yz by -y-z.

$$x=-\frac{1-yz}{y+z}$$

Solve for y

$$y=\frac{xz+1}{z-x}$$

$$x\neq z$$

Steps for Solving Linear Equation

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

$$x^{2}-xz-yx+yz=1+x^{2}$$

Subtract x^{2} from both sides.

$$-xz-yx+yz=1+x^{2}-x^{2}$$

Combine x^{2} and -x^{2} to get 0.

$$-xz-yx+yz=1$$

Add xz to both sides.

$$-yx+yz=1+xz$$

Combine all terms containing y.

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

The equation is in standard form.

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

Divide both sides by -x+z.

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

Dividing by -x+z undoes the multiplication by -x+z.

$$y=\frac{xz+1}{z-x}$$