What is (2(6/5))/(1-(6/5)^2) ?

The solution to (2(6/5))/(1-(6/5)^2) is -60/11

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simplify (2(6/5))/(1-(6/5)^2)

simplify

\frac{2 ( \frac{6}{5} )}{1 - ( \frac{6}{5} ) ^{2}}

- \frac{60}{11}

Decimal Notation

- 5.45454 \dots

Solution steps

\frac{2 ( \frac{6}{5} )}{1 - ( \frac{6}{5} ) ^{2}}

Apply rule:

(a) = a

(\frac{6}{5}) = \frac{6}{5}

= \frac{2 \cdot \frac{6}{5}}{1 - ( \frac{6}{5} ) ^{2}}

2 \cdot \frac{6}{5} = \frac{12}{5}

= \frac{\frac{12}{5}}{1 - ( \frac{6}{5} ) ^{2}}

Simplify

1 - (\frac{6}{5})^{2} : - \frac{11}{25}

= \frac{\frac{12}{5}}{- \frac{11}{25}}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{\frac{12}{5}}{\frac{11}{25}}

Apply the fraction rule:

\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a \cdot d}{b \cdot c}

\frac{\frac{12}{5}}{\frac{11}{25}} = \frac{12 \cdot 25}{5 \cdot 11}

= - \frac{12 \cdot 25}{5 \cdot 11}

Cancel

- \frac{12 \cdot 25}{5 \cdot 11} : - \frac{60}{11}

= - \frac{60}{11}

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