The expression 1/(1 - x) - 1/(1 + x) - x3/(1 - x) + x2/(1 + x) in lowe

1.	The expression 1/(1 - x) - 1/(1 + x) - x3/(1 - x) + x2/(1 + x) in lowest term is ……………A) x2 + 2x B) x2 – 2x C) x2+ 2 D) 2x + 1
Answer» Correct option is (A) x² + 2x \(\frac{1}{1-x}-\frac{1}{1+x}-\frac{x^3}{1-x}+\frac{x^2}{1+x}\) \(=\frac{1-x^3}{1-x}+\frac{x^2-1}{1+x}\) \(=\frac{(1-x)(1+x+x^2)}{1-x}+\frac{(1+x)(x-1)}{1+x}\) \(=1+x+x^2+x-1\) \(=2x+x^2\) Correct option is A) x² + 2x

The expression 1/(1 - x) - 1/(1 + x) - x3/(1 - x) + x2/(1 + x) in lowest term is ……………A) x2 + 2x B) x2 – 2x C) x2+ 2 D) 2x + 1

Answer»

Correct option is (A) x² + 2x

\(\frac{1}{1-x}-\frac{1}{1+x}-\frac{x^3}{1-x}+\frac{x^2}{1+x}\)

\(=\frac{1-x^3}{1-x}+\frac{x^2-1}{1+x}\)

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

\(=1+x+x^2+x-1\)

\(=2x+x^2\)

Correct option is A) x² + 2x