# Question #d7b37

Sep 22, 2016

$\frac{{x}^{2} - 6}{12 x + 9}$

#### Explanation:

Assumption: the given expression is meant to be:

$\frac{\frac{x}{3} - 2}{\frac{3}{x} ^ 2 + \frac{4}{x}}$

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$\textcolor{b l u e}{\text{Consider the numerator}}$

$\frac{x}{3} - 2 \to \frac{x}{3} - \frac{6}{3} \textcolor{b l u e}{= \frac{x - 6}{3}}$
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$\textcolor{b l u e}{\text{Consider the denominator}}$

$\frac{3}{x} ^ 2 + \frac{4}{x} \to \frac{3 x + 4 {x}^{2}}{x} ^ 2$
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$\textcolor{b l u e}{\text{Putting it all together}}$

$\frac{x - 6}{3} \div \frac{3 x + 4 {x}^{2}}{x} ^ 2$

$\frac{x - 6}{3} \times {x}^{2} / \left(3 x + 4 {x}^{2}\right) \text{ "=" } \frac{{x}^{3} - 6 {x}^{2}}{12 {x}^{2} + 9 x}$

Factor out $x$ from top and bottom.

$\frac{{\cancel{x}}^{1} \left({x}^{2} - 6\right)}{{\cancel{x}}^{1} \left(12 x + 9\right)}$