How do you combine $- \frac{8}{p} + \frac{p}{p + 5}$ $-8/p+p/(p+5)$ ?

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How do you combine $- \frac{8}{p} + \frac{p}{p + 5}$ $-8/p+p/(p+5)$ ?

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Answer 1 · 2017-03-15T21:59:03

$\frac{p^{2} - 8 p - 40}{p^{2} + 5 p}$ $(p^2-8p-40)/(p^2+5p)$

Explanation:

Switching the order round the other way:

$[\frac{p}{p + 5} \times 1] - [\frac{8}{p} \times 1]$ $color(green)([p/(p+5)color(red)(xx1)] -[8/pcolor(red)(xx1)] )$

$[\frac{p}{p + 5} \times \frac{p}{p}] - [\frac{8}{p} \times \frac{p + 5}{p + 5}]$ $color(green)([p/(p+5)color(red)(xxp/p)] -[8/pcolor(red)(xx(p+5)/(p+5))] )$

$[\frac{p^{2}}{p (p + 5)}] - [\frac{8 (p + 5)}{p (p + 5)}] \leftarrow denominators now the same$ $color(green)([p^2/(p(p+5))] -[(8(p+5))/(p(p+5))] larr" denominators now the same"$

$\frac{p^{2} - 8 (p + 5)}{p (p + 5)}$ $color(green)((p^2-8(p+5))/(p(p+5))$

$\frac{p^{2} - 8 p - 40}{p (p + 5)}$ $color(green)((p^2-8p-40)/(p(p+5)) )$

$\frac{p^{2} - 8 p - 40}{p^{2} + 5 p}$ $color(green)((p^2-8p-40)/(p^2+5p))$

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How do you combine $- \frac{8}{p} + \frac{p}{p + 5}$ $-8/p+p/(p+5)$ ?

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Explanation:

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How do you combine −8p+pp+5-8/p+p/(p+5)?

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How do you combine $- \frac{8}{p} + \frac{p}{p + 5}$ $-8/p+p/(p+5)$ ?