Simplify 5/(a^2+5a)-7/(3a+15)

$\frac{5}{a^{2} + 5 a} - \frac{7}{3 a + 15}$

Step 1

Simplify each term.

Factor $a$ out of $a^{2} + 5 a$ .

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

$\frac{5}{a \cdot a + 5 a} - \frac{7}{3 a + 15}$

Factor $a$ out of $5 a$ .

$\frac{5}{a \cdot a + a \cdot 5} - \frac{7}{3 a + 15}$

Factor $a$ out of $a \cdot a + a \cdot 5$ .

$\frac{5}{a (a + 5)} - \frac{7}{3 a + 15}$

Factor $3$ out of $3 a + 15$ .

Factor $3$ out of $3 a$ .

$\frac{5}{a (a + 5)} - \frac{7}{3 (a) + 15}$

Factor $3$ out of $15$ .

$\frac{5}{a (a + 5)} - \frac{7}{3 a + 3 \cdot 5}$

Factor $3$ out of $3 a + 3 \cdot 5$ .

$\frac{5}{a (a + 5)} - \frac{7}{3 (a + 5)}$

Step 2

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

$\frac{5}{a (a + 5)} \cdot \frac{3}{3} - \frac{7}{3 (a + 5)}$

Step 3

To write $- \frac{7}{3 (a + 5)}$ as a fraction with a common denominator, multiply by $\frac{a}{a}$ .

$\frac{5}{a (a + 5)} \cdot \frac{3}{3} - \frac{7}{3 (a + 5)} \cdot \frac{a}{a}$

Step 4

Write each expression with a common denominator of $a (a + 5) \cdot 3$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5}{a (a + 5)}$ by $\frac{3}{3}$ .

$\frac{5 \cdot 3}{a (a + 5) \cdot 3} - \frac{7}{3 (a + 5)} \cdot \frac{a}{a}$

Multiply $\frac{7}{3 (a + 5)}$ by $\frac{a}{a}$ .

$\frac{5 \cdot 3}{a (a + 5) \cdot 3} - \frac{7 a}{3 (a + 5) a}$

Reorder the factors of $a (a + 5) \cdot 3$ .

$\frac{5 \cdot 3}{3 a (a + 5)} - \frac{7 a}{3 (a + 5) a}$

Reorder the factors of $3 (a + 5) a$ .

$\frac{5 \cdot 3}{3 a (a + 5)} - \frac{7 a}{3 a (a + 5)}$

Step 5

Combine the numerators over the common denominator.

$\frac{5 \cdot 3 - 7 a}{3 a (a + 5)}$

Step 6

Multiply $5$ by $3$ .

$\frac{15 - 7 a}{3 a (a + 5)}$