# How do you solve for d in n= (dh)/(f+d)?

Jul 17, 2016

$\textcolor{g r e e n}{\frac{n f}{h - n} = d}$

#### Explanation:

To solve for $d$, we need to get it by itself (isolate the variable). First, undo the division by multiplying both sides by the denominator.

$n = \frac{\mathrm{dh}}{f + d}$

$\frac{f + d}{1} \cdot \frac{n}{1} = \frac{\mathrm{dh}}{\cancel{f + d}} \cdot \frac{\cancel{f + d}}{1}$

$\left(\left(f + d\right) \times n\right) = \mathrm{dh}$

$n f + n d = \mathrm{dh}$

Now get all terms with $d$ to one side and factor out the $d$.

$n f = \mathrm{dh} - n d$

$n f = d \left(h - n\right)$

Finish isolating the variable by getting $d$ by itself.

$\frac{n f}{h - n} = \frac{d \left(\cancel{h - n}\right)}{\cancel{h - n}}$

$\textcolor{g r e e n}{\frac{n f}{h - n} = d}$