Simplify (2a^2+10a)/(3a^2+15a)

$\frac{2 a^{2} + 10 a}{3 a^{2} + 15 a}$

Step 1

Factor $2 a$ out of $2 a^{2} + 10 a$ .

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

$\frac{2 a (a) + 10 a}{3 a^{2} + 15 a}$

Factor $2 a$ out of $10 a$ .

$\frac{2 a (a) + 2 a (5)}{3 a^{2} + 15 a}$

Factor $2 a$ out of $2 a (a) + 2 a (5)$ .

$\frac{2 a (a + 5)}{3 a^{2} + 15 a}$

$\frac{2 a (a + 5)}{3 a^{2} + 15 a}$

Step 2

Factor $3 a$ out of $3 a^{2} + 15 a$ .

Factor $3 a$ out of $3 a^{2}$ .

$\frac{2 a (a + 5)}{3 a (a) + 15 a}$

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

$\frac{2 a (a + 5)}{3 a (a) + 3 a (5)}$

Factor $3 a$ out of $3 a (a) + 3 a (5)$ .

$\frac{2 a (a + 5)}{3 a (a + 5)}$

$\frac{2 a (a + 5)}{3 a (a + 5)}$

Step 3

Cancel the common factor of $a$ .

Cancel the common factor.

$\frac{2 a (a + 5)}{3 a (a + 5)}$

Rewrite the expression.

$\frac{2 (a + 5)}{3 (a + 5)}$

$\frac{2 (a + 5)}{3 (a + 5)}$

Step 4

Cancel the common factor of $a + 5$ .

Cancel the common factor.

$\frac{2 (a + 5)}{3 (a + 5)}$

Rewrite the expression.

$\frac{2}{3}$

$\frac{2}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{3}$

Decimal Form:

$0.\overline{6}$

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