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

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) (Show Source): You can put this solution on YOUR website!
Solve for x:
I'm assuming that you have a typo in the term: and that it should read:, so, proceeding on that assumption:
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.
Applying the rule: If then
Subtract from both sides.
Add 16 to both sides.
Divide both sides by -8
which is choice B, however, when you substitute x = -4 into the original equation, you get:
Simplifying:
...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.
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