Solve by Factoring m/(m-7)-8=7/(m-7)

$\frac{m}{m - 7} - 8 = \frac{7}{m - 7}$

Step 1

Subtract $\frac{7}{m - 7}$ from both sides of the equation.

$\frac{m}{m - 7} - 8 - \frac{7}{m - 7} = 0$

Step 2

Simplify $\frac{m}{m - 7} - 8 - \frac{7}{m - 7}$ .

Find the common denominator.

Write $- 8$ as a fraction with denominator $1$ .

$\frac{m}{m - 7} + \frac{- 8}{1} - \frac{7}{m - 7} = 0$

Multiply $\frac{- 8}{1}$ by $\frac{m - 7}{m - 7}$ .

$\frac{m}{m - 7} + \frac{- 8}{1} \cdot \frac{m - 7}{m - 7} - \frac{7}{m - 7} = 0$

Multiply $\frac{- 8}{1}$ by $\frac{m - 7}{m - 7}$ .

$\frac{m}{m - 7} + \frac{- 8 (m - 7)}{m - 7} - \frac{7}{m - 7} = 0$

Combine the numerators over the common denominator.

$\frac{m - 8 (m - 7) - 7}{m - 7} = 0$

Simplify each term.

Apply the distributive property.

$\frac{m - 8 m - 8 \cdot - 7 - 7}{m - 7} = 0$

Multiply $- 8$ by $- 7$ .

$\frac{m - 8 m + 56 - 7}{m - 7} = 0$

Subtract $8 m$ from $m$ .

$\frac{- 7 m + 56 - 7}{m - 7} = 0$

Subtract $7$ from $56$ .

$\frac{- 7 m + 49}{m - 7} = 0$

Factor $7$ out of $- 7 m + 49$ .

Factor $7$ out of $- 7 m$ .

$\frac{7 (- m) + 49}{m - 7} = 0$

Factor $7$ out of $49$ .

$\frac{7 (- m) + 7 (7)}{m - 7} = 0$

Factor $7$ out of $7 (- m) + 7 (7)$ .

$\frac{7 (- m + 7)}{m - 7} = 0$

Cancel the common factor of $- m + 7$ and $m - 7$ .

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

$\frac{7 (- (m) + 7)}{m - 7} = 0$

Rewrite $7$ as $- 1 (- 7)$ .

$\frac{7 (- (m) - 1 (- 7))}{m - 7} = 0$

Factor $- 1$ out of $- (m) - 1 (- 7)$ .

$\frac{7 (- (m - 7))}{m - 7} = 0$

Rewrite $- (m - 7)$ as $- 1 (m - 7)$ .

$\frac{7 (- 1 (m - 7))}{m - 7} = 0$

Cancel the common factor.

$\frac{7 (- 1 (m - 7))}{m - 7} = 0$

Divide $7 \cdot (- 1)$ by $1$ .

$7 \cdot (- 1) = 0$

Multiply $7$ by $- 1$ .

$- 7 = 0$

Step 3

Since $- 7 \neq 0$ , there are no solutions.

No solution

Solve by Factoring m/(m-7)-8=7/(m-7)

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