Solve by Factoring 4/(x-4)=x/(x-4)-4/3

$\frac{4}{x - 4} = \frac{x}{x - 4} - \frac{4}{3}$

Step 1

Move all the expressions to the left side of the equation.

Subtract $\frac{x}{x - 4}$ from both sides of the equation.

$\frac{4}{x - 4} - \frac{x}{x - 4} = - \frac{4}{3}$

Add $\frac{4}{3}$ to both sides of the equation.

$\frac{4}{x - 4} - \frac{x}{x - 4} + \frac{4}{3} = 0$

Step 2

Simplify $\frac{4}{x - 4} - \frac{x}{x - 4} + \frac{4}{3}$ .

Combine the numerators over the common denominator.

$\frac{4 - x}{x - 4} + \frac{4}{3} = 0$

Cancel the common factor of $4 - x$ and $x - 4$ .

Rewrite $4$ as $- 1 (- 4)$ .

$\frac{- 1 (- 4) - x}{x - 4} + \frac{4}{3} = 0$

Factor $- 1$ out of $- x$ .

$\frac{- 1 (- 4) - (x)}{x - 4} + \frac{4}{3} = 0$

Factor $- 1$ out of $- 1 (- 4) - (x)$ .

$\frac{- 1 (- 4 + x)}{x - 4} + \frac{4}{3} = 0$

Reorder terms.

$\frac{- 1 (x - 4)}{x - 4} + \frac{4}{3} = 0$

Cancel the common factor.

$\frac{- 1 (x - 4)}{x - 4} + \frac{4}{3} = 0$

Divide $- 1$ by $1$ .

$- 1 + \frac{4}{3} = 0$

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- 1 \cdot \frac{3}{3} + \frac{4}{3} = 0$

Combine $- 1$ and $\frac{3}{3}$ .

$\frac{- 1 \cdot 3}{3} + \frac{4}{3} = 0$

Combine the numerators over the common denominator.

$\frac{- 1 \cdot 3 + 4}{3} = 0$

Simplify the numerator.

Multiply $- 1$ by $3$ .

$\frac{- 3 + 4}{3} = 0$

Add $- 3$ and $4$ .

$\frac{1}{3} = 0$

Step 3

Set the numerator equal to zero.

$1 = 0$

Step 4

Since $1 \neq 0$ , there are no solutions.

No solution