$$\frac{15}{p}+\frac{7p-9}{p+3} = 7$$

$$ \begin{aligned} \frac{15}{p}+\frac{7p-9}{p+3} &= 7&& \text{multiply ALL terms by } \color{blue}{ p(p+3) }. \\[1 em]p(p+3)\cdot\frac{15}{p}+p(p+3)\frac{7p-9}{p+3} &= p(p+3)\cdot7&& \text{cancel out the denominators} \\[1 em]15p+45+7p^2-9p &= 7p^2+21p&& \text{simplify left side} \\[1 em]7p^2+6p+45 &= 7p^2+21p&& \text{move all terms to the left hand side } \\[1 em]7p^2+6p+45-7p^2-21p &= 0&& \text{simplify left side} \\[1 em]7p^2+6p+45-7p^2-21p &= 0&& \\[1 em]-15p+45 &= 0&& \text{ move the constants to the right } \\[1 em]-15p &= -45&& \text{ divide both sides by $ -15 $ } \\[1 em]p &= \frac{-45}{-15}&& \\[1 em]p &= 3&& \\[1 em] \end{aligned} $$

This page was created using