Question

simplify.\frac{\frac{5x + 25}{3x}}{\frac{10x + 20}{x}}

Explanation:

Step1: Rewrite as multiplication by reciprocal

$\frac{5x+25}{3x} \times \frac{x}{10x+20}$

Step2: Factor numerators/denominators

$\frac{5(x+5)}{3x} \times \frac{x}{10(x+2)}$

Step3: Cancel common factors

$\frac{5(x+5)}{3\cancel{x}} \times \frac{\cancel{x}}{10(x+2)} = \frac{5(x+5)}{3 \times 10(x+2)}$

Step4: Simplify constant terms

$\frac{5(x+5)}{30(x+2)} = \frac{x+5}{6(x+2)}$

Answer:

$\frac{x+5}{6(x+2)}$