Simplify (4m-17)/(m^2-16)+(3m-11)/(m^2-16)

$\frac{4 m - 17}{m^{2} - 16} + \frac{3 m - 11}{m^{2} - 16}$

Step 1

Simplify terms.

Combine the numerators over the common denominator.

$\frac{4 m - 17 + 3 m - 11}{m^{2} - 16}$

Add $4 m$ and $3 m$ .

$\frac{7 m - 17 - 11}{m^{2} - 16}$

Subtract $11$ from $- 17$ .

$\frac{7 m - 28}{m^{2} - 16}$

Factor $7$ out of $7 m - 28$ .

Factor $7$ out of $7 m$ .

$\frac{7 (m) - 28}{m^{2} - 16}$

Factor $7$ out of $- 28$ .

$\frac{7 m + 7 \cdot - 4}{m^{2} - 16}$

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

$\frac{7 (m - 4)}{m^{2} - 16}$

Step 2

Simplify the denominator.

Rewrite $16$ as $4^{2}$ .

$\frac{7 (m - 4)}{m^{2} - 4^{2}}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = m$ and $b = 4$ .

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

Step 3

Cancel the common factor of $m - 4$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{7}{m + 4}$