# Question #b55d3

May 29, 2017

$2 \frac{p}{q} = - 3 \frac{p}{q} ^ 2 + \frac{5}{q} - 1$

#### Explanation:

Write as:$\text{ } 2 p = - 3 \frac{q}{p} - q + 5$

To 'force' the left hand side into the target format divide both sides by q.

$2 \frac{p}{q} = - 3 \frac{p}{q} ^ 2 - 1 + \frac{5}{q}$

Write as:

$2 \frac{p}{q} = - 3 \frac{p}{q} ^ 2 + \frac{5}{q} - 1$

May 29, 2017

Assuming $p , q \ne 0$, I got $\textcolor{red}{2 \frac{p}{q} = \frac{4 {p}^{2} / q + 2 p + 6}{5}}$

#### Explanation:

Given
$\textcolor{w h i t e}{\text{XXX}} 2 p + 3 \frac{q}{p} + q = 5$

Multiplying both sides by $\textcolor{b l u e}{\frac{p}{q}}$
$\textcolor{w h i t e}{\text{XXX}} 2 p \cdot \textcolor{b l u e}{\frac{p}{q}} + 3 \frac{q}{p} \cdot \textcolor{b l u e}{\frac{p}{q}} + q \cdot \textcolor{b l u e}{\frac{p}{q}} = 5 \cdot \textcolor{b l u e}{\frac{p}{q}}$

$\textcolor{w h i t e}{\text{XXX}} 2 {p}^{2} / q + 3 + p = 5 \frac{p}{q}$

Multiplying both sides by $\textcolor{g r e e n}{\frac{2}{5}}$
$\textcolor{w h i t e}{\text{XXX}} 2 {p}^{2} / q \cdot \textcolor{g r e e n}{\frac{2}{5}} + 3 \cdot \textcolor{g r e e n}{\frac{2}{5}} + p \cdot \textcolor{g r e e n}{\frac{2}{5}} = 5 \frac{p}{q} \cdot \textcolor{g r e e n}{\frac{2}{5}}$

$\textcolor{w h i t e}{\text{XXX}} \frac{4 {p}^{2} / q + 6 + 2 p}{5} = 2 \frac{p}{q}$

$\textcolor{w h i t e}{\text{XXX}} 2 \frac{p}{q} = \frac{4 {p}^{2} / q + 2 p + 6}{5}$