SOLUTION: Simplify and state any restrictions on the variables. (x)/(4x-8) - (x+1)/(x^2 + 2x - 8)

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Question 947128: Simplify and state any restrictions on the variables.
(x)/(4x-8) - (x+1)/(x^2 + 2x - 8)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
x%2F%284x-8%29-%28x%2B1%29%2F%28x%5E2+%2B+2x-8%29

x%2F%284%28x-2%29%29-%28x%2B1%29%2F%28x%5E2+-2x%2B+4x-8%29

x%2F%284%28x-2%29%29-%28x%2B1%29%2F%28%28x%5E2+-2x%29%2B+%284x-8%29%29

x%2F%284%28x-2%29%29-%28x%2B1%29%2F%28x%28x+-2%29%2B+4%28x-2%29%29

x%2F%284%28x-2%29%29-%28x%2B1%29%2F%28%28x%2B4%29%28x-2%29%29

x%28x%2B4%29%2F%284%28x-2%29%28x%2B4%29%29-4%28x%2B1%29%2F%284%28x%2B4%29%28x-2%29%29

%28x%28x%2B4%29-4%28x%2B1%29%29%2F%284%28x%2B4%29%28x-2%29%29

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

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

%28%28x-2%29%28x%2B2%29%29%2F%284%28x%2B4%29%28x-2%29%29

%28cross%28%28x-2%29%29%28x%2B2%29%29%2F%284%28x%2B4%29cross%28%28x-2%29%29%29%29

%28x%2B2%29%2F4%28x%2B4%29

a value of x that makes numerator equal to zero will be a real root:
if %28x%2B2%29=0=> highlight%28x=-2%29-> root

restrictions:

exclude a value of x that makes denominator equal to zero
%284x-8%29=>4x=8=>x=2
and
if %28x%2B4%29=0=> x=-4
so, { x element R : x%3C%3E-4 and x%3C%3E2 }


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%28x%2B2%29%2F4%28x%2B4%29%29+