Solve by Factoring 4/(m-8)=8/2

$\frac{4}{m - 8} = \frac{8}{2}$

Step 1

Subtract $\frac{8}{2}$ from both sides of the equation.

$\frac{4}{m - 8} - \frac{8}{2} = 0$

Step 2

Simplify $\frac{4}{m - 8} - \frac{8}{2}$ .

Simplify each term.

Divide $8$ by $2$ .

$\frac{4}{m - 8} - 1 \cdot 4 = 0$

Multiply $- 1$ by $4$ .

$\frac{4}{m - 8} - 4 = 0$

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{m - 8}{m - 8}$ .

$\frac{4}{m - 8} - 4 \cdot \frac{m - 8}{m - 8} = 0$

Combine $- 4$ and $\frac{m - 8}{m - 8}$ .

$\frac{4}{m - 8} + \frac{- 4 (m - 8)}{m - 8} = 0$

Combine the numerators over the common denominator.

$\frac{4 - 4 (m - 8)}{m - 8} = 0$

Simplify the numerator.

Factor $4$ out of $4 - 4 (m - 8)$ .

Factor $4$ out of $4$ .

$\frac{4 (1) - 4 (m - 8)}{m - 8} = 0$

Factor $4$ out of $- 4 (m - 8)$ .

$\frac{4 (1) + 4 (- (m - 8))}{m - 8} = 0$

Factor $4$ out of $4 (1) + 4 (- (m - 8))$ .

$\frac{4 (1 - (m - 8))}{m - 8} = 0$

Apply the distributive property.

$\frac{4 (1 - m - - 8)}{m - 8} = 0$

Multiply $- 1$ by $- 8$ .

$\frac{4 (1 - m + 8)}{m - 8} = 0$

Add $1$ and $8$ .

$\frac{4 (- m + 9)}{m - 8} = 0$

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

$\frac{4 (- (m) + 9)}{m - 8} = 0$

Rewrite $9$ as $- 1 (- 9)$ .

$\frac{4 (- (m) - 1 (- 9))}{m - 8} = 0$

Factor $- 1$ out of $- (m) - 1 (- 9)$ .

$\frac{4 (- (m - 9))}{m - 8} = 0$

Rewrite $- (m - 9)$ as $- 1 (m - 9)$ .

$\frac{4 (- 1 (m - 9))}{m - 8} = 0$

Move the negative in front of the fraction.

$- \frac{4 (m - 9)}{m - 8} = 0$

Step 3

Set the numerator equal to zero.

$4 (m - 9) = 0$

Step 4

Solve the equation for $m$ .

Divide each term in $4 (m - 9) = 0$ by $4$ and simplify.

Divide each term in $4 (m - 9) = 0$ by $4$ .

$\frac{4 (m - 9)}{4} = \frac{0}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 (m - 9)}{4} = \frac{0}{4}$

Divide $m - 9$ by $1$ .

$m - 9 = \frac{0}{4}$

Simplify the right side.

Divide $0$ by $4$ .

$m - 9 = 0$

Add $9$ to both sides of the equation.

$m = 9$

Solve by Factoring 4/(m-8)=8/2

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