# I need help with an algebra problem

#### Gretchen Vivanco

##### New member
I am having a problem with this:

r = ab/a+b solving for a

I started with multiplying both sides by (a+b)

to get r(a+b) = ab

then distributed the r

ra + rb = ab

then subtracted rb from both sides

ra = ab - rb

then divided by r on both sides

a = ab - rb/ r

I know the answer is a = br/b-r (from the back of the math book), but I have no idea how they got it!!

#### tkhunny

##### Moderator
Staff member
Gretchen Vivanco said:
then divided by r on both sides
Whoops. Don't do that. You are solving for 'a'. Gather them all up before complicating them.

ra = ab - rb

Subtract ab

ra - ab= - rb

Factor out the 'a'

a(r - b)= - rb

Personally, I'd multiply everythign by -1, just to simplify my life.

a(b - r)= rb

Divide by (b-r)

I think that will finish off the job.

#### Denis

##### Senior Member
Gretchen Vivanco said:
r = ab/a+b solving for a

CAREFUL! Brackets required: r = ab / (a + b)

You're ok to here:
ra = ab - rb

then divided by r on both sides : WHY?

Get the "a"'s together:
ab - ar = br
a(b - r) = br
a = br / (b - r) : kapish?

#### Gretchen Vivanco

##### New member
thank you!!

I am new to this posting thing, so I hope I am replying correctly!

Anyway, thank you all so much for your responses!! I was so pleasantly surprised!! I was so annoyed not knowing how to do that problem!