Question

simplify.\\(
\frac{
\frac{5x + 25}{2x^5}
}{
\frac{3x + 15}{x + 2}
}
\\)

Explanation:

Step1: Rewrite division as multiplication

$$\frac{\frac{5x+25}{2x^5}}{\frac{3x+15}{x+2}} = \frac{5x+25}{2x^5} \times \frac{x+2}{3x+15}$$

Step2: Factor numerators/denominators

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

Step3: Cancel common factors

$$\frac{5}{2x^5} \times \frac{x+2}{3}$$

Step4: Multiply remaining terms

$$\frac{5(x+2)}{6x^5} = \frac{5x+10}{6x^5}$$

Answer:

$\frac{5x+10}{6x^5}$ or $\frac{5(x+2)}{6x^5}$