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Let’s check out your problem:

(x-1)/(x+1)-(x+1)/(x-1) < 2

x−1x+1−x+1x−1<2 \frac{x-1}{x+1}-\frac{x+1}{x-1}<2

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Full solution

Q. x−1x+1−x+1x−1<2 \frac{x-1}{x+1}-\frac{x+1}{x-1}<2
  1. Find Common Denominator: Find a common denominator to combine the fractions.\newlineCommon denominator: (x+1)(x−1)(x+1)(x-1)\newline(x−1)(x−1)−(x+1)(x+1)(x+1)(x−1)<2\frac{(x-1)(x-1) - (x+1)(x+1)}{(x+1)(x-1)} < 2
  2. Expand Numerators: Expand the numerators. \newline(x2−2x+1)−(x2+2x+1)<2(x2−1)(x^2 - 2x + 1) - (x^2 + 2x + 1) < 2(x^2 - 1)
  3. Combine Like Terms: Combine like terms.\newline−x2−2x+1−x2−2x−1<2x2−2-x^2 - 2x + 1 - x^2 - 2x - 1 < 2x^2 - 2\newline−4x<2x2−2-4x < 2x^2 - 2
  4. Move Terms to One Side: Move all terms to one side. 2x2+4x−2>02x^2 + 4x - 2 > 0

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