SOLUTION: Add or subtract. Write the answer in lowest terms. x over x-4 plus 8 over x+4 minus 32 over x^2-16

Algebra ->  Equations -> SOLUTION: Add or subtract. Write the answer in lowest terms. x over x-4 plus 8 over x+4 minus 32 over x^2-16      Log On


   

Question 113385: Add or subtract. Write the answer in lowest terms.
x
over
x-4
plus
8
over
x+4
minus
32
over
x^2-16
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Write like this:
:
x%2F%28%28x-4%29%29 + 8%2F%28%28x%2B4%29%29 - 32%2F%28%28x%5E2-16%29%29
:
Note the 3rd denominator is the difference of squares, that we can factor:
x%2F%28%28x-4%29%29 + 8%2F%28%28x%2B4%29%29 - 32%2F%28%28x%2B4%29%28x-4%29%29
:
The common denominator would be (x-4)(x+4), so we have:
%28x%28x%2B4%29+%2B+8%28x-4%29+-+32%29%2F%28%28x-4%29%28x%2B4%29%29
:
Multiply what's inside the brackets:
%28x%5E2+%2B+4x+%2B+8x+-+32+-+32%29%2F%28%28x-4%29%28x%2B4%29%29
:
combine like terms and you have a quadratic, that we can factor:
%28x%5E2+%2B+12x+-+64%29%2F%28%28x-4%29%28x%2B4%29%29
:
%28%28x%2B16%29%28x-4%29%29%2F%28%28x-4%29%28x%2B4%29%29
:
The (x-4)'s cancel leaving us with:
%28%28x%2B16%29%29%2F%28%28x%2B4%29%29
:
How about this? Can you follow what went on here?