Simplify 30/(m^2-25)+3/(m-5)

$\frac{30}{m^{2} - 25} + \frac{3}{m - 5}$

Simplify the denominator.

Rewrite $25$ as $5^{2}$ .

$\frac{30}{m^{2} - 5^{2}} + \frac{3}{m - 5}$

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 $b = 5$ .

$\frac{30}{(m + 5) (m - 5)} + \frac{3}{m - 5}$

To write $\frac{3}{m - 5}$ as a fraction with a common denominator, multiply by $\frac{m + 5}{m + 5}$ .

$\frac{30}{(m + 5) (m - 5)} + \frac{3}{m - 5} \cdot \frac{m + 5}{m + 5}$

Write each expression with a common denominator of $(m + 5) (m - 5)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3}{m - 5}$ by $\frac{m + 5}{m + 5}$ .

$\frac{30}{(m + 5) (m - 5)} + \frac{3 (m + 5)}{(m - 5) (m + 5)}$

Reorder the factors of $(m - 5) (m + 5)$ .

$\frac{30}{(m + 5) (m - 5)} + \frac{3 (m + 5)}{(m + 5) (m - 5)}$

Combine the numerators over the common denominator.

$\frac{30 + 3 (m + 5)}{(m + 5) (m - 5)}$

Simplify the numerator.

Factor $3$ out of $30 + 3 (m + 5)$ .

Factor $3$ out of $30$ .

$\frac{3 \cdot 10 + 3 (m + 5)}{(m + 5) (m - 5)}$

Factor $3$ out of $3 \cdot 10 + 3 (m + 5)$ .

$\frac{3 (10 + m + 5)}{(m + 5) (m - 5)}$

Add $10$ and $5$ .

$\frac{3 (m + 15)}{(m + 5) (m - 5)}$