Simplify (6/(28x+4))÷(12/(35x+5))

$\frac{6}{28 x + 4} \div \frac{12}{35 x + 5}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{6}{28 x + 4} \cdot \frac{35 x + 5}{12}$

Step 2

Simplify terms.

Cancel the common factor of $6$ .

Factor $6$ out of $12$ .

$\frac{6}{28 x + 4} \cdot \frac{35 x + 5}{6 (2)}$

Cancel the common factor.

$\frac{6}{28 x + 4} \cdot \frac{35 x + 5}{6 \cdot 2}$

Rewrite the expression.

$\frac{1}{28 x + 4} \cdot \frac{35 x + 5}{2}$

Multiply $\frac{1}{28 x + 4}$ by $\frac{35 x + 5}{2}$ .

$\frac{35 x + 5}{(28 x + 4) \cdot 2}$

Factor $5$ out of $35 x + 5$ .

Factor $5$ out of $35 x$ .

$\frac{5 (7 x) + 5}{(28 x + 4) \cdot 2}$

Factor $5$ out of $5$ .

$\frac{5 (7 x) + 5 (1)}{(28 x + 4) \cdot 2}$

Factor $5$ out of $5 (7 x) + 5 (1)$ .

$\frac{5 (7 x + 1)}{(28 x + 4) \cdot 2}$

Step 3

Simplify the denominator.

Factor $4$ out of $28 x + 4$ .

Factor $4$ out of $28 x$ .

$\frac{5 (7 x + 1)}{(4 (7 x) + 4) \cdot 2}$

Factor $4$ out of $4$ .

$\frac{5 (7 x + 1)}{(4 (7 x) + 4 (1)) \cdot 2}$

Factor $4$ out of $4 (7 x) + 4 (1)$ .

$\frac{5 (7 x + 1)}{4 (7 x + 1) \cdot 2}$

Multiply $2$ by $4$ .

$\frac{5 (7 x + 1)}{8 (7 x + 1)}$

Step 4

Cancel the common factor of $7 x + 1$ .

Cancel the common factor.

$\frac{5 (7 x + 1)}{8 (7 x + 1)}$

Rewrite the expression.

$\frac{5}{8}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{8}$

Decimal Form:

$0.625$