# How do you solve \frac { 32} { h + 1} - \frac { 35} { h } = - 1?

May 10, 2017

h=7; h=-5

#### Explanation:

Given: $\frac{32}{h + 1} - \frac{35}{h} = - 1$

Multiply both sides by $h \left(h + 1\right)$:

$32 h \frac{\cancel{h + 1}}{\cancel{h + 1}} - 35 \cancel{h} \frac{h + 1}{\cancel{h}} = - h \left(h + 1\right)$

$32 h - 35 h - 35 = - {h}^{2} - h$

$- 3 h - 35 = - {h}^{2} - h$

${h}^{2} - 2 h - 35 = 0$

$\left(h - 7\right) \left(h + 5\right) = 0$

h=7; h=-5

To check, substitute answers into the $g i v e n$ equation:

$\frac{32}{h + 1} - \frac{35}{h} = - 1$

$\frac{32}{7 + 1} - \frac{35}{7} = - 1$

$4 - 5 = - 1$

$- 1 = - 1$

~~~~~

$\frac{32}{- 5 + 1} - \frac{35}{- 5} = - 1$

$\frac{32}{- 4} - \frac{35}{- 5} = - 1$

$- 8 + 7 = - 1$

$- 1 = - 1$