Simplify ((2a^2+14a)/(8a^2))÷(10a+70)

$\frac{2 a^{2} + 14 a}{8 a^{2}} \div (10 a + 70)$

Step 1

Rewrite the division as a fraction.

$\frac{\frac{2 a^{2} + 14 a}{8 a^{2}}}{10 a + 70}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{2 a^{2} + 14 a}{8 a^{2}} \cdot \frac{1}{10 a + 70}$

Step 3

Factor $2 a$ out of $2 a^{2} + 14 a$ .

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

$\frac{2 a (a) + 14 a}{8 a^{2}} \cdot \frac{1}{10 a + 70}$

Factor $2 a$ out of $14 a$ .

$\frac{2 a (a) + 2 a (7)}{8 a^{2}} \cdot \frac{1}{10 a + 70}$

Factor $2 a$ out of $2 a (a) + 2 a (7)$ .

$\frac{2 a (a + 7)}{8 a^{2}} \cdot \frac{1}{10 a + 70}$

Step 4

Cancel the common factor of $2$ and $8$ .

Factor $2$ out of $2 a (a + 7)$ .

$\frac{2 (a (a + 7))}{8 a^{2}} \cdot \frac{1}{10 a + 70}$

Cancel the common factors.

Factor $2$ out of $8 a^{2}$ .

$\frac{2 (a (a + 7))}{2 (4 a^{2})} \cdot \frac{1}{10 a + 70}$

Cancel the common factor.

$\frac{2 (a (a + 7))}{2 (4 a^{2})} \cdot \frac{1}{10 a + 70}$

Rewrite the expression.

$\frac{a (a + 7)}{4 a^{2}} \cdot \frac{1}{10 a + 70}$

Step 5

Cancel the common factors.

Factor $a$ out of $4 a^{2}$ .

$\frac{a (a + 7)}{a (4 a)} \cdot \frac{1}{10 a + 70}$

Cancel the common factor.

$\frac{a (a + 7)}{a (4 a)} \cdot \frac{1}{10 a + 70}$

Rewrite the expression.

$\frac{a + 7}{4 a} \cdot \frac{1}{10 a + 70}$

Step 6

Factor $10$ out of $10 a + 70$ .

Factor $10$ out of $10 a$ .

$\frac{a + 7}{4 a} \cdot \frac{1}{10 (a) + 70}$

Factor $10$ out of $70$ .

$\frac{a + 7}{4 a} \cdot \frac{1}{10 a + 10 \cdot 7}$

Factor $10$ out of $10 a + 10 \cdot 7$ .

$\frac{a + 7}{4 a} \cdot \frac{1}{10 (a + 7)}$

Step 7

Cancel the common factor of $a + 7$ .

Factor $a + 7$ out of $10 (a + 7)$ .

$\frac{a + 7}{4 a} \cdot \frac{1}{(a + 7) \cdot 10}$

Cancel the common factor.

$\frac{a + 7}{4 a} \cdot \frac{1}{(a + 7) \cdot 10}$

Rewrite the expression.

$\frac{1}{4 a} \cdot \frac{1}{10}$

Step 8

Multiply $\frac{1}{4 a}$ by $\frac{1}{10}$ .

$\frac{1}{4 a \cdot 10}$

Step 9

Multiply $10$ by $4$ .

$\frac{1}{40 a}$

Simplify ((2a^2+14a)/(8a^2))÷(10a+70)

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