Question

1. multiply.

\\(\frac{x^2}{x - 5} \cdot \frac{x^2 - 7x + 10}{x^2 + 3x}\\)
options:
\\(\frac{(x - 2)}{3x}\\)
1
\\(\frac{x - 2}{x + 3}\\)
\\(\frac{x(x - 2)}{x + 3}\\)

Explanation:

Step1: Factor all polynomials

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

Step2: Cancel common factors

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

Answer:

$\frac{x(x - 2)}{x + 3}$