SOLUTION: Hello! I have been frustrated by the following problem in my College Algebra online course where the following equation escapes simplification to the point indicated by the answ

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hello! I have been frustrated by the following problem in my College Algebra online course where the following equation escapes simplification to the point indicated by the answ      Log On


   

Question 44838: Hello!
I have been frustrated by the following problem in my College Algebra online course where the following equation escapes simplification to the point indicated by the answers in the back:
(x-1)/(x+1) - 2/(x^2+x)
(the book's answer is (x-2)/x
Would you know how one arrives (simplifies) to that result ?
thank you for your attention!
alex
Answer by adamchapman(301) About Me  (Show Source):
You can put this solution on YOUR website!
%28x-1%29%2F%28x%2B1%29+-+2%2F%28x%5E2%2Bx%29+
Notice that x%5E2%2Bx=x%28x%2B1%29
So:
%28x-1%29%2F%28x%2B1%29+-+2%2F%28x%5E2%2Bx%29+=%28x-1%29%2F%28x%2B1%29+-+2%2Fx%28x%2B1%29+
Now multiply top and bottom of the first fraction by x:
%28x%28x-1%29%29%2F%28x%28x%2B1%29%29+-+2%2F%28x%28x%2B1%29%29
And simplify:
%28x%28x-1%29-2%29%2F%28x%28x%2B1%29%29+
%28x%5E2-x-2%29%2F%28x%28x%2B1%29%29+
Factorise the top:
%28%28x%2B1%29%28x-2%29%29%2F%28x%28x%2B1%29%29+
The (X+1)'s cancel so:
%28x-2%29%2Fx+
Theres your answer. Dude!
I hope this helps.
P.S. I am trying to start up my own homework help website. I would be extremely grateful if you would e-mail me some feedback on the help you received to adam.chapman@student.manchester.ac.uk
Adam