# How do you simplify (36-1/x^2)/(1/(6x^2)-6)?

Oct 11, 2016

$= - 6$

#### Explanation:

The fractions need to be simplified into one term before you can continue with the division. Find the LCD in each case.

$\left(36 - \frac{1}{x} ^ 2\right) \div \left(\frac{1}{6 {x}^{2}} - 6\right)$

$= \left(\frac{36 {x}^{2} - 1}{x} ^ 2\right) \div \left(\frac{1 - 36 {x}^{2}}{6 {x}^{2}}\right)$

Change divide to multiply and invert the fraction.

$= \left(\frac{36 {x}^{2} - 1}{\cancel{{x}^{2}}}\right) \times \left(\frac{6 \cancel{{x}^{2}}}{1 - 36 {x}^{2}}\right)$

$= \left(36 {x}^{2} - 1\right) \times \frac{- 6}{\left(36 {x}^{2} - 1\right)} \text{ } \leftarrow$ note the sign switch-round

 =cancel((36x^2-1))xx(-6)/(cancel((36x^2-1))

$= - 6$

Oct 11, 2016

$\frac{36 - \frac{1}{{x}^{2}}}{\frac{1}{6 {x}^{2}} - 6} = \textcolor{g r e e n}{- 6}$

#### Explanation:

$36 - \frac{1}{{x}^{2}}$

$\textcolor{w h i t e}{\text{XXX}} = 6 \left(6 - \frac{1}{6 {x}^{2}}\right)$

$\textcolor{w h i t e}{\text{XXX}} = \left(- 6\right) \left(\frac{1}{6 {x}^{2}} - 6\right)$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$\frac{36 - \frac{1}{{x}^{2}}}{\frac{1}{6 {x}^{2}} - 6}$

$\textcolor{w h i t e}{\text{XXX}} = \frac{\left(- 6\right) \left(\frac{1}{6 {x}^{2}} - 1\right)}{\frac{1}{6 {x}^{2}} - 6}$

$\textcolor{w h i t e}{\text{XXX}} = - 6$