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

1.	Simplify \(\frac{1}{1+x+x^2}\) - \(\frac{1}{1-x+x^2}\) + \(\frac{2x}{1+x^2+x^4}\).............A) \(\frac{1}{1+x^2+x^4}\)B) 0 C) \(\frac{-1}{1+x^2+x^4}\)D) \(\frac{2x-3}{1+x^2+x^4}\)
Answer» Correct option is (B) 0 \(\frac{1}{1+x+x^2}-\frac{1}{1-x+x^2}+\frac{2x}{1+x^2+x^4}\) \(=\frac{(1-x+x^2)-(1+x+x^2)}{(1+x^2+x)(1+x^2-x)}+\frac{2x}{1+x^2+x^4}\) \(=\frac{-2x}{(1+x^2)^2-x^2}+\frac{2x}{1+x^2+x^4}\) \(=\frac{-2x}{1+x^4+2x^2-x^2}+\frac{2x}{1+x^2+x^4}\) \(=\frac{-2x}{1+x^2+x^4}+\frac{2x}{1+x^2+x^4}=0\) Correct option is B) 0

Simplify \(\frac{1}{1+x+x^2}\) - \(\frac{1}{1-x+x^2}\) + \(\frac{2x}{1+x^2+x^4}\).............A) \(\frac{1}{1+x^2+x^4}\)B) 0 C) \(\frac{-1}{1+x^2+x^4}\)D) \(\frac{2x-3}{1+x^2+x^4}\)

Answer»

Correct option is (B) 0

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

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

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

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

\(=\frac{-2x}{1+x^2+x^4}+\frac{2x}{1+x^2+x^4}=0\)

Correct option is B) 0