Solve by Factoring 1/(x-8)-1=7/(x-8)

$\frac{1}{x - 8} - 1 = \frac{7}{x - 8}$

Step 1

Subtract $\frac{7}{x - 8}$ from both sides of the equation.

$\frac{1}{x - 8} - 1 - \frac{7}{x - 8} = 0$

Step 2

Simplify $\frac{1}{x - 8} - 1 - \frac{7}{x - 8}$ .

Combine the numerators over the common denominator.

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

Subtract $7$ from $1$ .

$- 1 + \frac{- 6}{x - 8} = 0$

Move the negative in front of the fraction.

$- 1 - \frac{6}{x - 8} = 0$

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{x - 8}{x - 8}$ .

$- 1 \cdot \frac{x - 8}{x - 8} - \frac{6}{x - 8} = 0$

Combine $- 1$ and $\frac{x - 8}{x - 8}$ .

$\frac{- (x - 8)}{x - 8} - \frac{6}{x - 8} = 0$

Combine the numerators over the common denominator.

$\frac{- (x - 8) - 6}{x - 8} = 0$

Simplify the numerator.

Factor $- 1$ out of $- (x - 8) - 6$ .

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

$\frac{- (x - 8) - 1 (6)}{x - 8} = 0$

Factor $- 1$ out of $- (x - 8) - 1 (6)$ .

$\frac{- (x - 8 + 6)}{x - 8} = 0$

Add $- 8$ and $6$ .

$\frac{- (x - 2)}{x - 8} = 0$

Move the negative in front of the fraction.

$- \frac{x - 2}{x - 8} = 0$

Step 3

Set the numerator equal to zero.

$x - 2 = 0$

Step 4

Add $2$ to both sides of the equation.

$x = 2$