Solve Y=6x-6/x-6

$$Y = \frac { 6 x - 6 } { x - 6 }$$

Solve for x

$$x=-\frac{6\left(1-Y\right)}{Y-6}$$

$$Y\neq 6$$

Steps for Solving Linear Equation

Variable x cannot be equal to 6 since division by zero is not defined. Multiply both sides of the equation by x-6.

$$Y\left(x-6\right)=6x-6$$

Use the distributive property to multiply Y by x-6.

$$Yx-6Y=6x-6$$

Subtract 6x from both sides.

$$Yx-6Y-6x=-6$$

Add 6Y to both sides.

$$Yx-6x=-6+6Y$$

Combine all terms containing x.

$$\left(Y-6\right)x=-6+6Y$$

The equation is in standard form.

$$\left(Y-6\right)x=6Y-6$$

Divide both sides by Y-6.

$$\frac{\left(Y-6\right)x}{Y-6}=\frac{6Y-6}{Y-6}$$

Dividing by Y-6 undoes the multiplication by Y-6.

$$x=\frac{6Y-6}{Y-6}$$

Divide -6+6Y by Y-6.

$$x=\frac{6\left(Y-1\right)}{Y-6}$$

Variable x cannot be equal to 6.

$$x=\frac{6\left(Y-1\right)}{Y-6}\text{, }x\neq 6$$

Solve for Y

$$Y=-\frac{6\left(1-x\right)}{x-6}$$

$$x\neq 6$$