Help! Guitarist stuck on a math(s) problem! I'm sure this is embarrassingly basic for the folks around here, but I'm trying to rearrange this equation to give me $uw_2$ - is there anyone who could help? For the record, it's to try and help me figure out the unit weight of a string on a guitar from another string tuned to a different pitch. However, it's the maths bit I'm stuck on! Thanks in advance!
$$ ((uw_1*(2*sl*f_1)^2) / 386.4)/tl_1 - ((uw_1*(2*sl*f_2)^2) / 386.4)/tl_1 = ((uw_2*(2*sl*f_3)^2) / 386.4)/tl_2 - ((uw_2*(2*sl*f_4)^2) / 386.4)/tl_2 $$
 A: $$ \frac{uw_1\cdot(2\cdot sl\cdot f_1)^2}{386.4\cdot tl_1 }- \frac{uw_1\cdot (2\cdot sl \cdot f_2)^2)}{386.4\cdot tl_1} = \frac{uw_2 \cdot (2 \cdot sl \cdot f_3)^2}{386.4\cdot tl_2}- \frac{uw_2 \cdot (2 \cdot sl \cdot f_4)^2)}{386.4\cdot tl_2} \implies $$
$$ \frac{uw_1\cdot(2\cdot sl\cdot f_1)^2}{tl_1 }- \frac{uw_1\cdot (2\cdot sl \cdot f_2)^2)}{tl_1} = \frac{uw_2 \cdot (2 \cdot sl \cdot f_3)^2}{tl_2}- \frac{uw_2 \cdot (2 \cdot sl \cdot f_4)^2)}{tl_2} \implies $$
$$ \frac{uw_1\cdot(2\cdot sl\cdot f_1)^2}{tl_1 }- \frac{uw_1\cdot (2\cdot sl \cdot f_2)^2)}{tl_1} =uw_2 \cdot \left[ \frac{(2 \cdot sl \cdot f_3)^2}{tl_2}- \frac{(2 \cdot sl \cdot f_4)^2)}{tl_2}\right] \implies $$
$$ uw_2 = \frac{\frac{uw_1\cdot(2\cdot sl\cdot f_1)^2}{tl_1 }- \frac{uw_1\cdot (2\cdot sl \cdot f_2)^2)}{tl_1}}{\frac{(2 \cdot sl \cdot f_3)^2}{tl_2}- \frac{(2 \cdot sl \cdot f_4)^2)}{tl_2}} \implies $$
$$ uw_2 = uw_1\frac{\frac{f_1^2}{tl_1 }- \frac{f_2^2}{tl_1}}{\frac{f_3^2}{tl_2}- \frac{f_4^2}{tl_2}}=uw_1\frac{tl_2}{tl_1}\frac{f_1^2- f_2^2}{f_3^2- f_4^2}$$
EDIT: Just a side note, in future you should use variable names that are shorter, e.g. only one letter. Instead of using unit weight as $uw_1$ you could have written $w_1$, $tl=l$ and $sl=s$. It makes it easier to see what you have to do. 
A: I hit "enter" to get a new line but that posted the comment. I was then told that I could only edit a comment for 5 seconds!  So I decided to post the edited version as an "answer":
You can simplify that a lot by factoring out common terms: $\frac{4uw_1sl^2}{386.4tl_1}(f_1^2- f_2^2)= uw_2[\frac{4sl^2}{386.4tl_2}(f_3^2- f_4^2)]$.  Now divide both sides by $\frac{4sl^2}{386.4tl_2}(f_3^2- f_4^2)$.
A lot cancels.
