SOLUTION: I've been presented with this question: Solve the inequality [1/(x + 1)] > [1/(x � 1)]. State the solution set using interval notation. I started off by subtracting -[1/(x-1)]

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Question 134489: I've been presented with this question:
Solve the inequality [1/(x + 1)] > [1/(x � 1)]. State the solution set using interval notation.
I started off by subtracting -[1/(x-1)] from each side to get
[1/(x + 1)] - [1/(x � 1)] > 0
Then I got the common denominator of [1(x-1)/(x + 1)(x-1)] - [1(x+1)/(x+1)(x � 1)]
This results in [0/(x + 1)(x � 1)] which is 0. What am I doing wrong?
Answer by edjones(8007) (Show Source):
You can put this solution on YOUR website!
[1/(x + 1)] > [1/(x � 1)] LCD is (x+1)(x-1)
x-1>x+1 Multiply each side by LCD to eliminate fractions.
The equation is false because there is no number that when 1 is subtracted from it is larger than the same number when 1 is added to it.
X[]
The answer is the empty set.
.
Ed