ax + bx / (x + a)(x − b) =a + b/( x + c ) the 1st fraction has ax+bx as the numerator and a+b as the numerator for 2nd fraction.how did the a and b numerator vanish into =x/ (x + a)(x − b) = 1/ x + c

Question

How did this sudden shift happen, from ax+bx to x and a+b to 1?

Answer 1

First of all I want to warn you that your notation is unclear although you clarified by description.

You should have used more parentheses to clarify it.

Secondly, you have not told me what c is supposed to be. Is it just an undefined constant?

My first guess is that you should resolve the left side into partial fractions, but without a definition of c I am shooting in the dark.

BTW:

(a+b)x/[(x+a)(x-b)] = [a/x+a)] + [b/(x-b)]...but I am not sure that helps.

If you can add some more information to your question, then send me a message, I will try to help you further.