Simplify ((200+35x)/x)÷((250+40x)/x)

$\frac{200 + 35 x}{x} \div \frac{250 + 40 x}{x}$

To divide by a fraction, multiply by its reciprocal.

$\frac{200 + 35 x}{x} \cdot \frac{x}{250 + 40 x}$

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{200 + 35 x}{x} \cdot \frac{x}{250 + 40 x}$

Rewrite the expression.

$(200 + 35 x) \frac{1}{250 + 40 x}$

Factor $10$ out of $250 + 40 x$ .

Factor $10$ out of $250$ .

$(200 + 35 x) \frac{1}{10 (25) + 40 x}$

Factor $10$ out of $40 x$ .

$(200 + 35 x) \frac{1}{10 (25) + 10 (4 x)}$

Factor $10$ out of $10 (25) + 10 (4 x)$ .

$(200 + 35 x) \frac{1}{10 (25 + 4 x)}$

Multiply $200 + 35 x$ by $\frac{1}{10 (25 + 4 x)}$ .

$\frac{200 + 35 x}{10 (25 + 4 x)}$

Cancel the common factor of $200 + 35 x$ and $10$ .

Factor $5$ out of $200$ .

$\frac{5 (40) + 35 x}{10 (25 + 4 x)}$

Factor $5$ out of $35 x$ .

$\frac{5 (40) + 5 (7 x)}{10 (25 + 4 x)}$

Factor $5$ out of $5 (40) + 5 (7 x)$ .

$\frac{5 (40 + 7 x)}{10 (25 + 4 x)}$

Cancel the common factors.

Factor $5$ out of $10 (25 + 4 x)$ .

$\frac{5 (40 + 7 x)}{5 (2 (25 + 4 x))}$

Cancel the common factor.

$\frac{5 (40 + 7 x)}{5 (2 (25 + 4 x))}$

Rewrite the expression.

$\frac{40 + 7 x}{2 (25 + 4 x)}$