1. ## Re-arranging equation

Hi all,

Just a quick question trying to re-arrange a formula.

How do we do it when the subject we want is on both the top and the bottom in a fraction? An example would be something like the following.

Make R the subject.

$\displaystyle N = \frac{RM}{S + R}$ or something similar.

Any help is appreciated.

2. Originally Posted by Peleus
Hi all,

Just a quick question trying to re-arrange a formula.

How do we do it when the subject we want is on both the top and the bottom in a fraction? An example would be something like the following.

Make R the subject.

$\displaystyle N = \frac{RM}{S + R}$ or something similar.

Any help is appreciated.
start by multiplying both sides by the denominator on the right. you get $\displaystyle NS + NR = RM$

now how would you continue?

3. yeah, I can get that far.

From there you could divide by M which would result in R being on it's own on one side, but how do you get rid of the other R (part of NR)? That's the part I couldn't get. Typically to break it up you divide by N but then we're going backwards making the R which was on it's own $\displaystyle \frac{R}{N}$

4. Originally Posted by Peleus
yeah, I can get that far.

From there you could divide by M which would result in R being on it's own on one side, but how do you get rid of the other R (part of NR)? That's the part I couldn't get. Typically to break it up you divide by N but then we're going backwards making the R which was on it's own $\displaystyle \frac{R}{N}$
how about first bringing all the guys with R's in them on one side, and everything else on the other?

RM - NR = NS

but then R is a common factor on the left

R(M - N) = NS

and so...

5. Awesome,

The obvious answer staring me in the face, I just couldn't see it