Solve by Factoring m/(m-6)-7=6/(m-6)

$\frac{m}{m - 6} - 7 = \frac{6}{m - 6}$

Step 1

Subtract $\frac{6}{m - 6}$ from both sides of the equation.

$\frac{m}{m - 6} - 7 - \frac{6}{m - 6} = 0$

Step 2

Simplify $\frac{m}{m - 6} - 7 - \frac{6}{m - 6}$ .

Find the common denominator.

Write $- 7$ as a fraction with denominator $1$ .

$\frac{m}{m - 6} + \frac{- 7}{1} - \frac{6}{m - 6} = 0$

Multiply $\frac{- 7}{1}$ by $\frac{m - 6}{m - 6}$ .

$\frac{m}{m - 6} + \frac{- 7}{1} \cdot \frac{m - 6}{m - 6} - \frac{6}{m - 6} = 0$

Multiply $\frac{- 7}{1}$ by $\frac{m - 6}{m - 6}$ .

$\frac{m}{m - 6} + \frac{- 7 (m - 6)}{m - 6} - \frac{6}{m - 6} = 0$

Combine the numerators over the common denominator.

$\frac{m - 7 (m - 6) - 6}{m - 6} = 0$

Simplify each term.

Apply the distributive property.

$\frac{m - 7 m - 7 \cdot - 6 - 6}{m - 6} = 0$

Multiply $- 7$ by $- 6$ .

$\frac{m - 7 m + 42 - 6}{m - 6} = 0$

Subtract $7 m$ from $m$ .

$\frac{- 6 m + 42 - 6}{m - 6} = 0$

Subtract $6$ from $42$ .

$\frac{- 6 m + 36}{m - 6} = 0$

Factor $6$ out of $- 6 m + 36$ .

Factor $6$ out of $- 6 m$ .

$\frac{6 (- m) + 36}{m - 6} = 0$

Factor $6$ out of $36$ .

$\frac{6 (- m) + 6 (6)}{m - 6} = 0$

Factor $6$ out of $6 (- m) + 6 (6)$ .

$\frac{6 (- m + 6)}{m - 6} = 0$

Cancel the common factor of $- m + 6$ and $m - 6$ .

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

$\frac{6 (- (m) + 6)}{m - 6} = 0$

Rewrite $6$ as $- 1 (- 6)$ .

$\frac{6 (- (m) - 1 (- 6))}{m - 6} = 0$

Factor $- 1$ out of $- (m) - 1 (- 6)$ .

$\frac{6 (- (m - 6))}{m - 6} = 0$

Rewrite $- (m - 6)$ as $- 1 (m - 6)$ .

$\frac{6 (- 1 (m - 6))}{m - 6} = 0$

Cancel the common factor.

$\frac{6 (- 1 (m - 6))}{m - 6} = 0$

Divide $6 \cdot (- 1)$ by $1$ .

$6 \cdot (- 1) = 0$

Multiply $6$ by $- 1$ .

$- 6 = 0$

Step 3

Since $- 6 \neq 0$ , there are no solutions.

No solution

Solve by Factoring m/(m-6)-7=6/(m-6)

Related Questions

Support LCMGCF.com by disabling your adblocker.