Question
$$\frac{1}{h+5} = \frac{-h}{h-40}$$
Answer
$$ \begin{matrix}h_1 = 4 & h_2 = -10 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{1}{h+5} &= \frac{-h}{h-40}&& \text{multiply ALL terms by } \color{blue}{ (h+5)(h-40) }. \\[1 em](h+5)(h-40)\cdot\frac{1}{h+5} &= (h+5)(h-40)\frac{-h}{h-40}&& \text{cancel out the denominators} \\[1 em]h-40 &= -h^2-5h&& \text{move all terms to the left hand side } \\[1 em]h-40+h^2+5h &= 0&& \text{simplify left side} \\[1 em]h^2+6h-40 &= 0&& \\[1 em] \end{aligned} $$
$ x^{2}+6x-40 = 0 $ is a quadratic equation.
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