Expert: Bobby Soltani - 8/3/2004

Question
if y=ab divided by a+b , then b equals  ?

or   y= ab
       __
       a+b      then b equals

Answer
Hi Kristin,

Here are the steps you can use to solve for b.  Remember that if you do something to one side, you must do it to the other to keep the expression balanced.

y = (ab)/(a+b)
multiply both sides by a+b
y*(a+b) = ab
ya+yb = ab
subtract ab from each side
ya+yb-ab = 0
group the two terms with b together and factor out the b.
ya + b*(y-a) = 0
subtract ya from each side to isolate the b term.
b*(y-a) = -ya
divide both sides by (y-a)
b = (-ya)/(y-a)
This is the answer.  If you dont like the negative sign at the top of the answer, you can multiple the top and bottom by -1.  Since you are doing that to the top and the bottom, it is the same as multiplying it by 1 because -1/-1 = 1.

So, the answer could also be written as

b = (-1)(-ya)/((-1)(y-a)) = (ya)/(a-y)
b = (ya)/(a-y)

I hope this helps you out.  Good Luck.

Bobby