Simplify (4(5/x)+3)/(5(5/x)+2)

$\frac{4 (\frac{5}{x}) + 3}{5 (\frac{5}{x}) + 2}$

Step 1

Simplify the numerator.

Multiply $4 \frac{5}{x}$ .

Combine $4$ and $\frac{5}{x}$ .

$\frac{\frac{4 \cdot 5}{x} + 3}{5 \frac{5}{x} + 2}$

Multiply $4$ by $5$ .

$\frac{\frac{20}{x} + 3}{5 \frac{5}{x} + 2}$

To write $3$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{\frac{20}{x} + \frac{3 x}{x}}{5 \frac{5}{x} + 2}$

Combine the numerators over the common denominator.

$\frac{\frac{20 + 3 x}{x}}{5 \frac{5}{x} + 2}$

Step 2

Simplify the denominator.

Multiply $5 \frac{5}{x}$ .

Combine $5$ and $\frac{5}{x}$ .

$\frac{\frac{20 + 3 x}{x}}{\frac{5 \cdot 5}{x} + 2}$

Multiply $5$ by $5$ .

$\frac{\frac{20 + 3 x}{x}}{\frac{25}{x} + 2}$

To write $2$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{\frac{20 + 3 x}{x}}{\frac{25}{x} + \frac{2 x}{x}}$

Combine the numerators over the common denominator.

$\frac{\frac{20 + 3 x}{x}}{\frac{25 + 2 x}{x}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{20 + 3 x}{x} \cdot \frac{x}{25 + 2 x}$

Step 4

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{20 + 3 x}{x} \cdot \frac{x}{25 + 2 x}$

Rewrite the expression.

$(20 + 3 x) \frac{1}{25 + 2 x}$

Step 5

Multiply $20 + 3 x$ by $\frac{1}{25 + 2 x}$ .

$\frac{20 + 3 x}{25 + 2 x}$