Algebra Examples

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

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

Tap for more steps...

Step 2.1

Find the common denominator.

Tap for more steps...

Step 2.1.1

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

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

Step 2.1.2

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

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

Step 2.1.3

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

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

Step 2.2

Combine the numerators over the common denominator.

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

Step 2.3

Simplify each term.

Tap for more steps...

Step 2.3.1

Apply the distributive property.

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

Step 2.3.2

Multiply $- 7$ by $- 6$ .

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

Step 2.4

Subtract $7 m$ from $m$ .

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

Step 2.5

Subtract $6$ from $42$ .

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

Step 2.6

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

Tap for more steps...

Step 2.6.1

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

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

Step 2.6.2

Factor $6$ out of $36$ .

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

Step 2.6.3

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

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

Step 2.7

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

Tap for more steps...

Step 2.7.1

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

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

Step 2.7.2

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

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

Step 2.7.3

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

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

Step 2.7.4

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

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

Step 2.7.5

Cancel the common factor.

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

Step 2.7.6

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

$6 \cdot (- 1) = 0$

Step 2.8

Multiply $6$ by $- 1$ .

$- 6 = 0$

Step 3

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

No solution