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

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

Step 1

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

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

Step 2

Simplify $\frac{m}{m - 4} - 5 - \frac{4}{m - 4}$ .

Find the common denominator.

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

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

Multiply $\frac{- 5}{1}$ by $\frac{m - 4}{m - 4}$ .

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

Multiply $\frac{- 5}{1}$ by $\frac{m - 4}{m - 4}$ .

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

Combine the numerators over the common denominator.

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

Simplify each term.

Apply the distributive property.

$\frac{m - 5 m - 5 \cdot - 4 - 4}{m - 4} = 0$

Multiply $- 5$ by $- 4$ .

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

Subtract $5 m$ from $m$ .

$\frac{- 4 m + 20 - 4}{m - 4} = 0$

Subtract $4$ from $20$ .

$\frac{- 4 m + 16}{m - 4} = 0$

Factor $4$ out of $- 4 m + 16$ .

Factor $4$ out of $- 4 m$ .

$\frac{4 (- m) + 16}{m - 4} = 0$

Factor $4$ out of $16$ .

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

Factor $4$ out of $4 (- m) + 4 (4)$ .

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

Cancel the common factor of $- m + 4$ and $m - 4$ .

Factor $- 1$ out of $- m$ .

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

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

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

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

$\frac{4 (- (m - 4))}{m - 4} = 0$

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

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

Cancel the common factor.

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

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 m/(m-4)-5=4/(m-4)

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