Simplify \(\cfrac{x+1}{x-1}\) + \(\cfrac{x-1}{x+1}\) - \(\cfrac{2

1.	Simplify \(\cfrac{x+1}{x-1}\) + \(\cfrac{x-1}{x+1}\) - \(\cfrac{2x^2-2}{x^2+1}\)A) \(\cfrac{4x^4+2}{x^4-1}\)B) \(\cfrac{8x^2}{x^4-1}\)C) \(\cfrac{4x^2}{x^4-1}\)D) 1
Answer» Correct option is (B) \(\frac{8x^2}{x^4-1}\) \(\frac{x+1}{x-1}+\frac{x-1}{x+1}-\frac{2x^2-2}{x^2+1}\) \(=\frac{(x+1)^2(x^2+1)+(x-1)^2(x^2+1)-2(x^2-1)(x^2-1)}{(x-1)(x+1)(x^2+1)}\) \(=\frac{(x^2+1)(x^2+2x+1+x^2-2x+1)-2(x^2-1)^2)}{(x^2-1)(x^2+1)}\) \(=\frac{2(x^2+1)^2\div2(x^2-1)^2}{z^4-1}\) \(=\frac{2(x^4+2x^2+1-(x^4-2x^2+1))}{z^4-1}\) \(=\frac{8x^2}{x^4-1}\) Correct option is B) \(\cfrac{8x^2}{x^4-1}\)

Simplify \(\cfrac{x+1}{x-1}\) + \(\cfrac{x-1}{x+1}\) - \(\cfrac{2x^2-2}{x^2+1}\)A) \(\cfrac{4x^4+2}{x^4-1}\)B) \(\cfrac{8x^2}{x^4-1}\)C) \(\cfrac{4x^2}{x^4-1}\)D) 1

Answer»

Correct option is (B) \(\frac{8x^2}{x^4-1}\)

\(\frac{x+1}{x-1}+\frac{x-1}{x+1}-\frac{2x^2-2}{x^2+1}\)

\(=\frac{(x+1)^2(x^2+1)+(x-1)^2(x^2+1)-2(x^2-1)(x^2-1)}{(x-1)(x+1)(x^2+1)}\)

\(=\frac{(x^2+1)(x^2+2x+1+x^2-2x+1)-2(x^2-1)^2)}{(x^2-1)(x^2+1)}\)

\(=\frac{2(x^2+1)^2\div2(x^2-1)^2}{z^4-1}\)

\(=\frac{2(x^4+2x^2+1-(x^4-2x^2+1))}{z^4-1}\)

\(=\frac{8x^2}{x^4-1}\)

Correct option is B) \(\cfrac{8x^2}{x^4-1}\)