# Solve for a. c=(ab) / (a+b)

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`c=(ab)/(a+b)` solve for a

first multiply both sides by (a+b) to get rid of fraction

`c(a+b)=ab`

Now distribute

`ac+bc=ab`

Now we want to get all the terms with a as a factor on one side and everything else on the other

`ac-ab=-bc`

now factor out the a

`a(c-b)=-bc`

Now divide by `c-b`

`a=-(bc)/(c-b)`

And we can get rid of the negative sign by noting `(c-b)=-(b-c)`

To get our final answer `a = (bc)/(b-c)`

c=(ab) / (a+b)

Get rid of the fraction:

c (a + b) = ab

ac + bc = ab Distributive Property

ac - ab = -bc Isolating the variable we want to one side

a (c - b) = = -bc

a = -bc / (c-b)