Solve y=1/x-5

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

Solve for x

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

$$y\neq 0$$

Steps for Solving Linear Equation

Variable x cannot be equal to 5 since division by zero is not defined. Multiply both sides of the equation by x-5.

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

Use the distributive property to multiply y by x-5.

$$yx-5y=1$$

Add 5y to both sides.

$$yx=1+5y$$

The equation is in standard form.

$$yx=5y+1$$

Divide both sides by y.

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

Dividing by y undoes the multiplication by y.

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

Divide 1+5y by y.

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

Variable x cannot be equal to 5.

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

Solve for y

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

$$x\neq 5$$