Solve y^-1=5+x

$$y ^ { - 1 } = 5 + x$$

Solve for y

$$y=\frac{1}{x+5}$$

$$x\neq -5$$

Steps for Solving Linear Equation

Reorder the terms.

$$\frac{1}{y}=x+5$$

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by y.

$$1=yx+y\times 5$$

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

$$yx+y\times 5=1$$

Combine all terms containing y.

$$\left(x+5\right)y=1$$

Divide both sides by x+5.

$$\frac{\left(x+5\right)y}{x+5}=\frac{1}{x+5}$$

Dividing by x+5 undoes the multiplication by x+5.

$$y=\frac{1}{x+5}$$

Variable y cannot be equal to 0.

$$y=\frac{1}{x+5}\text{, }y\neq 0$$

Solve for x

$$x=-5+\frac{1}{y}$$

$$y\neq 0$$