Solve x/3-2/m-3=1

$$\frac { x } { 3 } - \frac { 2 } { m - 3 } = 1$$

Solve for m

$$m=-\frac{3\left(x-1\right)}{3-x}$$

$$x\neq 3$$

Steps for Solving Linear Equation

Variable m cannot be equal to 3 since division by zero is not defined. Multiply both sides of the equation by 3\left(m-3\right), the least common multiple of 3,m-3.

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

Use the distributive property to multiply m-3 by x.

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

Multiply -3 and 2 to get -6.

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

Use the distributive property to multiply 3 by m-3.

$$mx-3x-6=3m-9$$

Subtract 3m from both sides.

$$mx-3x-6-3m=-9$$

Add 3x to both sides.

$$mx-6-3m=-9+3x$$

Add 6 to both sides.

$$mx-3m=-9+3x+6$$

Add -9 and 6 to get -3.

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

Combine all terms containing m.

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

The equation is in standard form.

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

Divide both sides by x-3.

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

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

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

Divide -3+3x by x-3.

$$m=\frac{3\left(x-1\right)}{x-3}$$

Variable m cannot be equal to 3.

$$m=\frac{3\left(x-1\right)}{x-3}\text{, }m\neq 3$$

Solve for x

$$x=-\frac{3\left(1-m\right)}{m-3}$$

$$m\neq 3$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3\left(m-3\right), the least common multiple of 3,m-3.

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

Use the distributive property to multiply m-3 by x.

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

Multiply -3 and 2 to get -6.

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

Use the distributive property to multiply 3 by m-3.

$$mx-3x-6=3m-9$$

Add 6 to both sides.

$$mx-3x=3m-9+6$$

Add -9 and 6 to get -3.

$$mx-3x=3m-3$$

Combine all terms containing x.

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

Divide both sides by m-3.

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

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

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

Divide -3+3m by m-3.

$$x=\frac{3\left(m-1\right)}{m-3}$$