Solve m=x-3/x-6+2

$$m = \frac { x - 3 } { x - 6 } + 2$$

Solve for x

$$x=-\frac{3\left(2m-5\right)}{3-m}$$

$$m\neq 3$$

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.

$$m\left(x-6\right)=x-3+\left(x-6\right)\times 2$$

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

$$mx-6m=x-3+\left(x-6\right)\times 2$$

Use the distributive property to multiply x-6 by 2.

$$mx-6m=x-3+2x-12$$

Combine x and 2x to get 3x.

$$mx-6m=3x-3-12$$

Subtract 12 from -3 to get -15.

$$mx-6m=3x-15$$

Subtract 3x from both sides.

$$mx-6m-3x=-15$$

Add 6m to both sides.

$$mx-3x=-15+6m$$

Combine all terms containing x.

$$\left(m-3\right)x=-15+6m$$

The equation is in standard form.

$$\left(m-3\right)x=6m-15$$

Divide both sides by m-3.

$$\frac{\left(m-3\right)x}{m-3}=\frac{6m-15}{m-3}$$

Dividing by m-3 undoes the multiplication by m-3.

$$x=\frac{6m-15}{m-3}$$

Divide 6m-15 by m-3.

$$x=\frac{3\left(2m-5\right)}{m-3}$$

Variable x cannot be equal to 6.

$$x=\frac{3\left(2m-5\right)}{m-3}\text{, }x\neq 6$$

Solve for m

$$m=-\frac{3\left(5-x\right)}{x-6}$$

$$x\neq 6$$