Question

assuming that no denominator equals zero, what is the simplest form of this expression?\\(\frac{\frac{x + 2}{6x}}{\frac{x + 2}{2x^2}}\\)\
enter the correct answer in the box.

Explanation:

Step1: Rewrite division as multiplication

$\frac{\frac{x+2}{6x}}{\frac{x+2}{2x^2}} = \frac{x+2}{6x} \times \frac{2x^2}{x+2}$

Step2: Cancel common factors

Cancel $(x+2)$; simplify $\frac{2x^2}{6x} = \frac{2}{6} \times \frac{x^2}{x}$

Step3: Simplify coefficients and exponents

$\frac{2}{6} = \frac{1}{3}$, $\frac{x^2}{x} = x$; combine to get $\frac{1}{3}x$

Answer:

$\frac{x}{3}$