Solve y=x+5/x-1

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

Solve for x

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

$$y\neq 1$$

Steps for Solving Linear Equation

Variable x cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by x-1.

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

Use the distributive property to multiply y by x-1.

$$yx-y=x+5$$

Subtract x from both sides.

$$yx-y-x=5$$

Add y to both sides.

$$yx-x=5+y$$

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by y-1.

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

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

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

Variable x cannot be equal to 1.

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

Solve for y

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

$$x\neq 1$$