# How do you solve 6/(11v)+6/v=1?

Feb 16, 2016

$v = \frac{72}{11} \to 6 \frac{6}{11}$

#### Explanation:

Given:$\text{ } \frac{6}{11 v} + \frac{6}{v} = 1$

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Write as:$\text{ } \frac{1}{v} \left(\frac{6}{11} + \frac{66}{11}\right) = 1$

$\frac{1}{v} \left(\frac{72}{11}\right) = \frac{1}{1} \text{ }$

$\textcolor{b r o w n}{\text{note that "1/1" is another way of writing 1 . I did this so }}$
$\textcolor{b r o w n}{\text{that you did not have any mental blocks about inverting 1}}$

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$\textcolor{b l u e}{\text{Turn everything upside down!}}$

$v \left(\frac{11}{72}\right) = 1$

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$\textcolor{b l u e}{\text{To get rid of "11/72" on the left hand side multiply "underline("both sides")" by } \textcolor{m a \ge n t a}{\frac{72}{11}}}$

$\textcolor{b r o w n}{\text{To get rid of something in 'multiply or divide' turn it into 1}}$

$v \times \frac{11}{72} \textcolor{m a \ge n t a}{\times \frac{72}{11}} = 1 \textcolor{m a \ge n t a}{\times \frac{72}{11}}$

$v \times \frac{11}{11} \times \frac{72}{72} = \frac{72}{11}$

$\textcolor{b r o w n}{\text{But "11/11" and "72/72" both equal to 1}}$

$v \times 1 \times 1 = \frac{72}{11}$

$v = \frac{72}{11} \to 6 \frac{6}{11}$