SOLUTION: Need This Tonight! Simplify this expression and state any restrictions. Thanks for any help! [(x + 1)/(x^2 + 2x - 8)] - [(x)/(4x - 8)]

Algebra ->  Expressions-with-variables -> SOLUTION: Need This Tonight! Simplify this expression and state any restrictions. Thanks for any help! [(x + 1)/(x^2 + 2x - 8)] - [(x)/(4x - 8)]      Log On


   

Question 713404: Need This Tonight! Simplify this expression and state any restrictions. Thanks for any help!
[(x + 1)/(x^2 + 2x - 8)] - [(x)/(4x - 8)]
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28x+%2B+1%29%2F%28x%5E2+%2B+2x+-+8%29+-+%28x%29%2F%284x+-+8%29

%28x+%2B+1%29%2F%28%28x%2B4%29%28x+-+2%29%29+-+%28x%29%2F%284x+-+8%29

%28x+%2B+1%29%2F%28%28x%2B4%29%28x+-+2%29%29+-+%28x%29%2F%284%28x+-+2%29%29

%284%28x+%2B+1%29%29%2F%284%28x%2B4%29%28x+-+2%29%29+-+%28x%29%2F%284%28x+-+2%29%29

%284x+%2B+4%29%2F%284%28x%2B4%29%28x+-+2%29%29+-+%28x%29%2F%284%28x+-+2%29%29





%284x+%2B+4-%28x%5E2%2B4x%29%29%2F%284%28x%2B4%29%28x+-+2%29%29

%284x+%2B+4-x%5E2-4x%29%2F%284%28x%2B4%29%28x+-+2%29%29

%28-x%5E2%2B4%29%2F%284%28x%2B4%29%28x+-+2%29%29

%28-%28x%5E2-4%29%29%2F%284%28x%2B4%29%28x+-+2%29%29

%28-%28x+-+2%29%28x+%2B+2%29%29%2F%284%28x%2B4%29%28x+-+2%29%29

-%28x+%2B+2%29%2F%284%28x%2B4%29%29

-%28x+%2B+2%29%2F%284x%2B16%29

================================================================
So

%28x+%2B+1%29%2F%28x%5E2+%2B+2x+-+8%29+-+%28x%29%2F%284x+-+8%29

simplifies to

-%28x+%2B+2%29%2F%284x%2B16%29

To avoid dividing by zero, we must make the following restrictions: x%3C%3E-4 and x%3C%3E2