SOLUTION: Okay, only four problems left for my homework assignment and I cannot figure them out (go figure). I am suppose to solve the rational equations, and I can not seem to get the right

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Okay, only four problems left for my homework assignment and I cannot figure them out (go figure). I am suppose to solve the rational equations, and I can not seem to get the right      Log On


   

Question 132126: Okay, only four problems left for my homework assignment and I cannot figure them out (go figure). I am suppose to solve the rational equations, and I can not seem to get the right answer for this one
x/x+4[-]4/a-4=x^2+16/x^2-16
I do know that the answer has to be one of these
A) 0
B) -4
C) no solution
D) 4
I placed the - in [] just so you could tell the difference between the two fractions, it does not mean anything.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
I'm assuming that you have a typo in the term:4%2F%28a-4%29 and that it should read:4%2F%28x-4%29, so, proceeding on that assumption:
%28x%2F%28x%2B4%29%29-%284%2F%28x-4%29%29+=+%28x%5E2%2B16%29%2F%28x%5E2-16%29 Simplify the fractions on the left side by finding the common denominator of (x+4)(x-4):
On the left side, simplify the numerator and perform the indicated multiplication in the denominator.
%28x%5E2-4x-4x-16%29%2F%28x%5E2-16%29+=+%28x%5E2%2B16%29%2F%28x%5E2-16%29 Applying the rule: Ifa%2Fb+=+c%2Fb then a+=+c
x%5E2-8x-16+=+x%5E2%2B16 Subtract x%5E2 from both sides.
-8x-16+=+16 Add 16 to both sides.
-8x+=+32 Divide both sides by -8
x+=+-4 which is choice B, however, when you substitute x = -4 into the original equation, you get:
Simplifying:
%28%28-4%29%2F0%29-%284%2F%28-8%29%29+=+%2832%2F0%29...and, as you know, division by zero is not defined and thefore, not permitted.
So the solution would have to be NO SOLUTION or choice C.