# Math Help - rearranging formulae with fractions

1. ## rearranging formulae with fractions

how would i do this

y=mx+x/2m

2. Originally Posted by maths noob
how would i do this

y=mx+x/2m
Do you want to solve for x, y or m ?

$y = mx + \frac{x}{2m}$

3. ooops x

4. Originally Posted by maths noob
ooops x
Because x is in both terms it can be factored out:

$
y = mx + \frac{x}{2m} = x\left(m+\frac{1}{2m}\right)
$

Divide through to isolate x:

$x = \frac{y}{\left(m+\frac{1}{2m}\right)}$

That can be tidied up by multiplying through by $2m$

$x = \frac{2my}{2m^2+1}$