SOLUTION: perform the indicated operation. simplify show step by step ILL USE " / " to represent the equation. it does not mean to DIVIDE. ""/"" ---MEANS--over NOT divide 5/2-x+ 2x/

Algebra ->  Equations -> SOLUTION: perform the indicated operation. simplify show step by step ILL USE " / " to represent the equation. it does not mean to DIVIDE. ""/"" ---MEANS--over NOT divide 5/2-x+ 2x/      Log On


   

Question 372035: perform the indicated operation. simplify show step by step
ILL USE " / " to represent the equation. it does not mean to DIVIDE.
""/"" ---MEANS--over NOT divide
5/2-x+ 2x/ x^2-4 - 1/2+x
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
I assume you mean:
5%2F%28%282-x%29%29+%2B+%282x%29%2F%28%28x%5E2-4%29%29+-+1%2F%28%282%2Bx%29%29
:
You can factor x^2-4 as the difference of squares
5%2F%28%282-x%29%29+%2B+%282x%29%2F%28%28x-2%29%28x%2B2%29%29+-+1%2F%28%282%2Bx%29%29
:
make the other denominators compatible
5%2F%28-1%28x-2%29%29+%2B+%282x%29%2F%28%28x-2%29%28x%2B2%29%29+-+1%2F%28%28x%2B2%29%29
:
the -1 just changes the sign of the 1st term
-5%2F%28%28x-2%29%29+%2B+%282x%29%2F%28%28x-2%29%28x%2B2%29%29+-+1%2F%28%28x%2B2%29%29
:
The common denominator is (x-2)(x+2) so we have
%28-5%28x%2B2%29+%2B+2x+-+%28x-2%29%29%2F%28%28x%2B2%29%28x-2%29%29 = %28-5x+-+10+%2B+2x+-+x+%2B+2%29%2F%28%28x%2B2%29%28x-2%29%29 = %28-4x+-+8%29%2F%28%28x%2B2%29%28x-2%29%29
:
Factor the numerator, cancel (x+2)
%28-4%28x+%2B+2%29%29%2F%28%28x%2B2%29%28x-2%29%29 = %28-4%29%2F%28%28x-2%29%29