To solve the equation 1/x-1 + 1/x+1 = 2/x^2-1, we can start by finding a common denominator for the fractions on the left side.
The common denominator for 1/(x-1) and 1/(x+1) is (x-1)(x+1). Rewriting the equation with this common denominator, we have:
[(x+1)+(x-1)] / (x-1)(x+1) = 2/(x^2-1)
Simplifying the numerator and denominator:
[2x] / (x-1)(x+1) = 2/(x^2-1)
Now, we can cancel out the (x^2-1) terms:
[2x] / (x-1)(x+1) = 2/[(x-1)(x+1)]
Since the numerators (2x) and the denominators (x-1)(x+1) are the same on both sides, we can equate them:
2x = 2
Solving for x:
2x = 2
x = 1
Therefore, the solution to the equation is x = 1.
Solve the following equation. If the equation has no solution so state.
1/x-1 + 1/x+1 = 2/x^2-1
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