SOLUTION: Please help! I have to simplify a rational expression, and I don't know how to get to the end result. Could you please show me how to do this step by step? The expression is {{{

Algebra ->  Equations -> SOLUTION: Please help! I have to simplify a rational expression, and I don't know how to get to the end result. Could you please show me how to do this step by step? The expression is {{{      Log On


   

Question 101312This question is from textbook Beginning Algebra
: Please help! I have to simplify a rational expression, and I don't know how to get to the end result. Could you please show me how to do this step by step?
The expression is %284-%281%2Fx%5E2%29%29%2F%282%2B%281%2Fx%29%29
I can only simplify it up to %284x%5E2-1%29%2F%282x%5E2%2Bx%29 and I don't know if what I did up to there is correct. In any case it's not the final solution.
The final solution given in my book is %282x-1%29%2Fx
Thanks ahead very much for helping me to get there! This question is from textbook Beginning Algebra

Found 3 solutions by Earlsdon, MathLover1, edjones:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify:
%284-%281%2Fx%5E2%29%29%2F%282%2B%281%2Fx%29%29 Your first step was very good!
%284x%5E2-1%29%2F%282x%5E2%2Bx%29 Now you can factor the numerator and factor an x from the denominator.
cross%28%282x%2B1%29%29%282x-1%29%2F%28x%2Across%28%282x%2B1%29%29%29 Cancel the indicated factors to leave you with:
%282x-1%29%2Fx

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
The expression is %284-%281%2Fx%5E2%29%29%2F%282%2B%281%2Fx%29%29
You already simplified it up to %284x%5E2-1%29%2F%282x%5E2%2Bx%29 which is correct.

Now you can write your nominator this way:
4x^2 – 1= (2x)^2 -1=(2x -1)(2x+1)
With denominator we can do following: 2x^2+x=x(2x+1)

Now, we will have:
%282x+-1%29%282x%2B1%29%2F+x%282x%2B1%29
now eliminate both (2x+1), and
final result will be:
%282x+-1%29%2F+%0D%0A++++x

Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
%284-%281%2Fx%5E2%29%29%2F%282%2B%281%2Fx%29%29
=%28%284x%5E2-1%29%2Fx%5E2%29%2F%28%282x%2B1%29%2Fx%29 LCD top=x^2 bottom=x
=%28%282x-1%29cross%282x%2B1%29%2Fx%5E2%29%2A%28x%2Fcross%282x%2B1%29%29Factor (4x^2-1), then multiply fractions then do cancelation.
=%282x-1%29%2Fx
Ed