# Rearranging formulas

## Main Question or Discussion Point

just revising for gcse's and there always seems to be a question with three unknown denominators and you have to rearrange the equation

they are usually like
1/a+1/b=1/c
make b the subject of the formula
can you explain how to do this

symbolipoint
Homework Helper
Gold Member
Based on your wording, what you want is not clear. Are you trying to solve the equation for b? You need to understand and know how to use the properties of real numbers. You will find an equation that is equivalent to your given one. I would start by multiplying both sides of the equation by the common denominator, abc.

1/a+1/b=1/c
1/b=1/c-1/a
b=1/(1/c-1/a)

If you want to continue to simplify it further:
b=1/(1/c-1/a)
b=ac/(a-c)

That is generally considered more simplified, but how simplified is necessary completely depends on the application.

\begin{align*} \frac 1 a + \frac 1 b & = \frac 1 c \\ abc\left(\frac 1 a + \frac 1 b\right) & = \frac{abc}{c} \\ \frac{abc}{a} + \frac{abc}{b} & = ab \\ bc + ac & = ab \\ ac & = ab-bc = b(a-c)\\ \frac{ac}{a-c} & = b \end{align*}