Solve y(x+y)-x=y(y+1)+1

$$y(x+y)-x=y(y+1)+1$$

Solve for x

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

$$y\neq 1$$

Steps for Solving Linear Equation

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

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

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

$$yx+y^{2}-x=y^{2}+y+1$$

Subtract y^{2} from both sides.

$$yx-x=y^{2}+y+1-y^{2}$$

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

$$yx-x=y+1$$

Combine all terms containing x.

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

Divide both sides by y-1.

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

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

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

Solve for y

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

$$x\neq 1$$

Steps for Solving Linear Equation

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

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

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

$$yx+y^{2}-x=y^{2}+y+1$$

Subtract y^{2} from both sides.

$$yx+y^{2}-x-y^{2}=y+1$$

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

$$yx-x=y+1$$

Subtract y from both sides.

$$yx-x-y=1$$

Add x to both sides.

$$yx-y=1+x$$

Combine all terms containing y.

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

The equation is in standard form.

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

Divide both sides by x-1.

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

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

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