# How do you solve for do in (hi)/(ho)=-(di)/(do) ?

Sep 3, 2016

$\left(\mathrm{do}\right) = - \frac{h o \times \mathrm{di}}{h i}$

#### Explanation:

If an equation has one fraction on each side, you can get rid of the denominators by cross-multiplying.

$\frac{h i}{h o} = - \frac{\mathrm{di}}{\textcolor{red}{\mathrm{do}}}$

$h i \times \textcolor{red}{\mathrm{do}} = - h o \times \mathrm{di} \text{ "larr div } \left(h i\right)$

$\textcolor{red}{\mathrm{do}} = - \frac{h o \times \mathrm{di}}{h i}$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
If an equation has one fraction on each side, you can invert the whole equation. This will put $\mathrm{do}$ in the numerator.

$\frac{h o}{h i} = - \frac{\textcolor{red}{\mathrm{do}}}{\mathrm{di}} \text{ } \leftarrow \times - \mathrm{di}$

$- \frac{h o \times \mathrm{di}}{h i} = \textcolor{red}{\mathrm{do}}$

$\textcolor{red}{\mathrm{do}} = - \frac{h o \times \mathrm{di}}{h i}$