Expert: Richard J. Raridon - 8/15/2010

Question
Hi, I'm having trouble with this problem. I have an answer key to check my work but I don't know how to get to it. I've been trying and I'm not understanding what I'm doing. The problem is 5/x+5-4x/(x+1)(x+5). I thought you had to multiply the first fraction by (x+1) on the top and bottom of the fraction so that the denominators of both fractions would be the same but past that I don't know how they reduce it down to get the answer 1/x+1. Could you please help me by explaining it? Thank you.

Answer
Well, in the first place, to avoid confusion, it should have been written 5/(x+5) -4x/[(x+1)(x+5)]
You were correct to multiply the first term by (x+1) top and bottom to get (5x+5)/[(x+1)(x+5)]  
Now if you combine the numerators you have 5x+5-4x which = (x+5).
That cancels the (x+5) in the denominator and leaves you 1/(x+1)