Solve by Factoring 5/(x-5)=x/(x-5)-5/4

$\frac{5}{x - 5} = \frac{x}{x - 5} - \frac{5}{4}$

Step 1

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

Subtract $\frac{x}{x - 5}$ from both sides of the equation.

$\frac{5}{x - 5} - \frac{x}{x - 5} = - \frac{5}{4}$

Add $\frac{5}{4}$ to both sides of the equation.

$\frac{5}{x - 5} - \frac{x}{x - 5} + \frac{5}{4} = 0$

Step 2

Simplify $\frac{5}{x - 5} - \frac{x}{x - 5} + \frac{5}{4}$ .

Combine the numerators over the common denominator.

$\frac{5 - x}{x - 5} + \frac{5}{4} = 0$

Cancel the common factor of $5 - x$ and $x - 5$ .

Rewrite $5$ as $- 1 (- 5)$ .

$\frac{- 1 (- 5) - x}{x - 5} + \frac{5}{4} = 0$

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

$\frac{- 1 (- 5) - (x)}{x - 5} + \frac{5}{4} = 0$

Factor $- 1$ out of $- 1 (- 5) - (x)$ .

$\frac{- 1 (- 5 + x)}{x - 5} + \frac{5}{4} = 0$

Reorder terms.

$\frac{- 1 (x - 5)}{x - 5} + \frac{5}{4} = 0$

Cancel the common factor.

$\frac{- 1 (x - 5)}{x - 5} + \frac{5}{4} = 0$

Divide $- 1$ by $1$ .

$- 1 + \frac{5}{4} = 0$

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- 1 \cdot \frac{4}{4} + \frac{5}{4} = 0$

Combine $- 1$ and $\frac{4}{4}$ .

$\frac{- 1 \cdot 4}{4} + \frac{5}{4} = 0$

Combine the numerators over the common denominator.

$\frac{- 1 \cdot 4 + 5}{4} = 0$

Simplify the numerator.

Multiply $- 1$ by $4$ .

$\frac{- 4 + 5}{4} = 0$

Add $- 4$ and $5$ .

$\frac{1}{4} = 0$

Step 3

Set the numerator equal to zero.

$1 = 0$

Step 4

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

No solution