Question

form. $\frac{x^{2}+x - 20}{3x^{2}-12x}cdot\frac{3x - 15}{5x^{2}-25x}$
$\frac{(x + 5)}{x}cdot\frac{1}{5x}=\frac{x + 5}{5x^{2}}$
$\frac{1}{x}cdot\frac{1}{5x}=\frac{1}{5x^{2}}$
$\frac{(x - 5)}{3x}cdot\frac{1}{5x}=\frac{x - 5}{15x^{2}}$
$\frac{(x + 5)}{3x}cdot\frac{1}{5x}=\frac{x + 5}{15x^{2}}$
steps:

1. factor all terms
2. reduce common terms
3. multiply & write in simplest factored form

Explanation:

Step1: Factor the expressions

• Factor $x^{2}+x - 20=(x + 5)(x-4)$
• Factor $3x^{2}-12x = 3x(x - 4)$
• Factor $3x-15=3(x - 5)$
• Factor $5x^{2}-25x=5x(x - 5)$

So the original expression $\frac{x^{2}+x - 20}{3x^{2}-12x}\cdot\frac{3x - 15}{5x^{2}-25x}=\frac{(x + 5)(x - 4)}{3x(x - 4)}\cdot\frac{3(x - 5)}{5x(x - 5)}$

Step2: Reduce common terms

Cancel out the common terms $(x - 4)$ and $(x - 5)$ in the numerator and denominator.
We get $\frac{x + 5}{3x}\cdot\frac{3}{5x}$

Step3: Multiply the remaining terms

$\frac{x + 5}{3x}\cdot\frac{3}{5x}=\frac{3(x + 5)}{15x^{2}}=\frac{x + 5}{5x^{2}}$

Answer:

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