Alg1.2.10

Find the sum of the rational expressions $\frac{x+1}{(x-1)^2}\,$ and $\frac{1}{x+1}\,$

The sum of the given expressions is

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

Simplifying,we have the expression as

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

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

$\frac{2x^2+2}{x^3+x^2-2x^2-2x+x+1}=\frac{2x^2+2}{x^3-x^2-x+1}\,$