Simplify 5/m-(m+8)/(m^2-4m)

$\frac{5}{m} - \frac{m + 8}{m^{2} - 4 m}$

Step 1

Factor $m$ out of $m^{2} - 4 m$ .

Factor $m$ out of $m^{2}$ .

$\frac{5}{m} - \frac{m + 8}{m \cdot m - 4 m}$

Factor $m$ out of $- 4 m$ .

$\frac{5}{m} - \frac{m + 8}{m \cdot m + m \cdot - 4}$

Factor $m$ out of $m \cdot m + m \cdot - 4$ .

$\frac{5}{m} - \frac{m + 8}{m (m - 4)}$

Step 2

To write $\frac{5}{m}$ as a fraction with a common denominator, multiply by $\frac{m - 4}{m - 4}$ .

$\frac{5}{m} \cdot \frac{m - 4}{m - 4} - \frac{m + 8}{m (m - 4)}$

Step 3

Simplify terms.

Multiply $\frac{5}{m}$ by $\frac{m - 4}{m - 4}$ .

$\frac{5 (m - 4)}{m (m - 4)} - \frac{m + 8}{m (m - 4)}$

Combine the numerators over the common denominator.

$\frac{5 (m - 4) - (m + 8)}{m (m - 4)}$

Step 4

Simplify the numerator.

Apply the distributive property.

$\frac{5 m + 5 \cdot - 4 - (m + 8)}{m (m - 4)}$

Multiply $5$ by $- 4$ .

$\frac{5 m - 20 - (m + 8)}{m (m - 4)}$

Apply the distributive property.

$\frac{5 m - 20 - m - 1 \cdot 8}{m (m - 4)}$

Multiply $- 1$ by $8$ .

$\frac{5 m - 20 - m - 8}{m (m - 4)}$

Subtract $m$ from $5 m$ .

$\frac{4 m - 20 - 8}{m (m - 4)}$

Subtract $8$ from $- 20$ .

$\frac{4 m - 28}{m (m - 4)}$

Factor $4$ out of $4 m - 28$ .

Factor $4$ out of $4 m$ .

$\frac{4 (m) - 28}{m (m - 4)}$

Factor $4$ out of $- 28$ .

$\frac{4 m + 4 \cdot - 7}{m (m - 4)}$

Factor $4$ out of $4 m + 4 \cdot - 7$ .

$\frac{4 (m - 7)}{m (m - 4)}$