Question

1. multiply: \\(\boldsymbol{\frac{x^2 - 6x}{x^2 - 36} cdot \frac{x + 6}{x^2}}\\)

options:
\\(\boldsymbol{\frac{x}{x + 6}}\\)
\\(\boldsymbol{\frac{1}{x}}\\)
\\(\boldsymbol{\frac{x - 6}{x + 6}}\\)
\\(\boldsymbol{\frac{x}{x^2}}\\)

Explanation:

Step1: Factor numerators/denominators

$\frac{x(x-6)}{(x-6)(x+6)} \cdot \frac{x+6}{x^2}$

Step2: Cancel common factors

$\frac{x\cancel{(x-6)}}{\cancel{(x-6)}\cancel{(x+6)}} \cdot \frac{\cancel{x+6}}{x^2} = \frac{1}{x}$

Answer:

$\frac{x-6}{x(x+6)}$ (Note: If the last option is $\frac{x-6}{x^2}$ due to image clarity, adjust accordingly; assuming standard simplification: $\frac{x(x-6)}{(x-6)(x+6)} \cdot \frac{x+6}{x^2} = \frac{1}{x}$ if all factors cancel, but based on visible options, likely $\frac{1}{x}$ is the correct choice)