Question #b55d3

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Question #b55d3

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Answer 1 · 2017-05-29T11:28:07

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

Explanation:

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

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

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

Write as:

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

Answer 2 · 2017-05-29T11:31:29

Assuming $p, q \neq 0$ $p,q!=0$ , I got $2 \frac{p}{q} = \frac{4 \frac{p^{2}}{q} + 2 p + 6}{5}$ $color(red)(2p/q=(4p^2/q+2p+6)/5)$

Explanation:

Given
$XXX 2 p + 3 \frac{q}{p} + q = 5$ $color(white)("XXX")2p+3q/p+q=5$

Multiplying both sides by $\frac{p}{q}$ $color(blue)(p/q)$
$XXX 2 p \cdot \frac{p}{q} + 3 \frac{q}{p} \cdot \frac{p}{q} + q \cdot \frac{p}{q} = 5 \cdot \frac{p}{q}$ $color(white)("XXX")2p * color(blue)(p/q) +3q/p * color(blue)(p/q) + q * color(blue)(p/q) = 5 * color(blue)(p/q)$

$XXX 2 \frac{p^{2}}{q} + 3 + p = 5 \frac{p}{q}$ $color(white)("XXX")2p^2/q+3+p=5p/q$

Multiplying both sides by $\frac{2}{5}$ $color(green)(2/5)$
$XXX 2 \frac{p^{2}}{q} \cdot \frac{2}{5} + 3 \cdot \frac{2}{5} + p \cdot \frac{2}{5} = 5 \frac{p}{q} \cdot \frac{2}{5}$ $color(white)("XXX")2p^2/q * color(green)(2/5)+3 * color(green)(2/5) +p * color(green)(2/5) = 5p/q * color(green)(2/5)$

$XXX \frac{4 \frac{p^{2}}{q} + 6 + 2 p}{5} = 2 \frac{p}{q}$ $color(white)("XXX")(4p^2/q+6+2p)/5=2p/q$

$XXX 2 \frac{p}{q} = \frac{4 \frac{p^{2}}{q} + 2 p + 6}{5}$ $color(white)("XXX")2p/q=(4p^2/q+2p+6)/5$

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Question #b55d3

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