OK, Priscilla, let's see.
I think this is what the question is: (x+a)/a=(b+c)/c. In words, this is: the sum of x and a divided by a equals the sum of b and c divided by c. Is that right? Treat a, b and c as if you knew what numbers they represent,
We want to end up with x on one side of the equals and a, b and c on the other.
We need to get rid of the fractions. On the left we have a in the denominator, so if we multiply both sides by a, the one on the left will cancel out: x+a=a(b+c)/c. Now expand the right side: x+a=(ab+ac)/c. We still need to get the a on the left over to the right, so we subtract a from each side:
x=(ab+ac)/c - a.
Now we have a fraction and a whole number on the right. We need to combine these by placing everything over the same denominator, c. Now, a is the same as a/1, so we divide 1 into c and we get c, of course, so we multiply c by the numerator a to give ac (ac/c=a). What we have now is: x=(ab+ac-ac)/c. So ac cancels out and we're left with x=ab/c.
Alternatively, cross-multiply: c(x+a)=a(b+c); cx+ca=ab+ac. ca=ac so these terms cancel: cx=ab, x=ab/c.
I've presented this answer as simply as I can, so I apologise if it's too simple, and you may be able to skip a couple of steps if you understand what's going on.