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

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

Step 1

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

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

Step 2

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

Find the common denominator.

Write $- 5$ as a fraction with denominator $1$ .

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

Multiply $\frac{- 5}{1}$ by $\frac{x - 5}{x - 5}$ .

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

Multiply $\frac{- 5}{1}$ by $\frac{x - 5}{x - 5}$ .

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

Combine the numerators over the common denominator.

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

Simplify each term.

Apply the distributive property.

$\frac{x - 5 x - 5 \cdot - 5 - 5}{x - 5} = 0$

Multiply $- 5$ by $- 5$ .

$\frac{x - 5 x + 25 - 5}{x - 5} = 0$

Subtract $5 x$ from $x$ .

$\frac{- 4 x + 25 - 5}{x - 5} = 0$

Subtract $5$ from $25$ .

$\frac{- 4 x + 20}{x - 5} = 0$

Factor $4$ out of $- 4 x + 20$ .

Factor $4$ out of $- 4 x$ .

$\frac{4 (- x) + 20}{x - 5} = 0$

Factor $4$ out of $20$ .

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

Factor $4$ out of $4 (- x) + 4 (5)$ .

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

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

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

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

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

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

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

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

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

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

Cancel the common factor.

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

Divide $4 \cdot (- 1)$ by $1$ .

$4 \cdot (- 1) = 0$

Multiply $4$ by $- 1$ .

$- 4 = 0$

Step 3

Since $- 4 \neq 0$ , there are no solutions.

No solution

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

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