Simplify ((170+50x)/x)÷((120+30x)/x)

$\frac{170 + 50 x}{x} \div \frac{120 + 30 x}{x}$

To divide by a fraction, multiply by its reciprocal.

$\frac{170 + 50 x}{x} \cdot \frac{x}{120 + 30 x}$

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{170 + 50 x}{x} \cdot \frac{x}{120 + 30 x}$

Rewrite the expression.

$(170 + 50 x) \frac{1}{120 + 30 x}$

Factor $30$ out of $120 + 30 x$ .

Factor $30$ out of $120$ .

$(170 + 50 x) \frac{1}{30 \cdot 4 + 30 x}$

Factor $30$ out of $30 \cdot 4 + 30 x$ .

$(170 + 50 x) \frac{1}{30 (4 + x)}$

Multiply $170 + 50 x$ by $\frac{1}{30 (4 + x)}$ .

$\frac{170 + 50 x}{30 (4 + x)}$

Cancel the common factor of $170 + 50 x$ and $30$ .

Factor $10$ out of $170$ .

$\frac{10 (17) + 50 x}{30 (4 + x)}$

Factor $10$ out of $50 x$ .

$\frac{10 (17) + 10 (5 x)}{30 (4 + x)}$

Factor $10$ out of $10 (17) + 10 (5 x)$ .

$\frac{10 (17 + 5 x)}{30 (4 + x)}$

Cancel the common factors.

Factor $10$ out of $30 (4 + x)$ .

$\frac{10 (17 + 5 x)}{10 (3 (4 + x))}$

Cancel the common factor.

$\frac{10 (17 + 5 x)}{10 (3 (4 + x))}$

Rewrite the expression.

$\frac{17 + 5 x}{3 (4 + x)}$