# Question #881a0

Feb 24, 2017

$h = - \frac{4}{7}$

#### Explanation:

To eliminate the fractions in the equation, multiply ALL terms on both sides by the $\textcolor{b l u e}{\text{lowest common multiple}}$ (LCM) of the denominators 4, 2 and 8

the LCM of 4, 2 and 8 is 8

$\Rightarrow \left({\cancel{8}}^{2} \times \frac{5 h}{\cancel{4}} ^ 1\right) + \left({\cancel{8}}^{4} \times \frac{1}{\cancel{2}} ^ 1\right) = \left({\cancel{8}}^{1} \times \frac{3 h}{\cancel{8}} ^ 1\right)$

$\Rightarrow 10 h + 4 = 3 h \leftarrow \textcolor{red}{\text{no fractions}}$

subtract 3h from both sides.

$10 h - 3 h + 4 = \cancel{3 h} \cancel{- 3 h}$

$\Rightarrow 7 h + 4 = 0$

subtract 4 from both sides.

$7 h \cancel{+ 4} \cancel{- 4} = 0 - 4$

$\Rightarrow 7 h = - 4$

divide both sides by 7

$\frac{\cancel{7} h}{\cancel{7}} = \frac{- 4}{7}$

$\Rightarrow h = - \frac{4}{7} \text{ is the solution}$