math help!?

Question

i seriously need help. this type of problem is gonna be on a test tomorrow and i don't get it!!!

(ab+bc) * 1/b - (ac-bc) * 1/c + (ac+ba)

p.s. the answer is c-a

Answer 1

Are you sure thats the equation?
((ab+bc)/b) - ((ac-bc)/c) + (ac+ ba)
=(b(a+c))/b) - (c(a-b))/c + a(c+b)
=a+c - a + b + a(c+b)
=0 +(c+b)+a(c+b)
=(c+b)(1+a) Not (c-a)

Answer 2

You just need to multiply everything out to simple the expression. If helps to break it down into terms:
(ab+bc)*1/b = ab*1/b + bc*1/b = a + c similarly:
(ac - bc) * 1/c = a -b
(ac + ab) = ac + ab
Therefore:
(a+c) - (a - b) + (ac + ab) = a + c - a + b + ac + ab
= c + b + ac + ab = c(1+a) + b (1+a) =
(1+a) * (c +b)

Answer 3

I got the same answer as the one above. i did not get c-a. perhaps the notation is incorrect in your question.

a + c -a + b +ac + ab = c + b +ac +ab
c(1+a) +b(1+a)=
(1+a)(c+b)