Alg1.2.11

Find the sum of $\frac{x^2+x-1}{x^2-1}\,$ and $\frac{x+1}{x^3+2}\,$

Sum of the expressions can be expressed as

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

Now simplifying the above expression

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

$\frac{(x^5+x^4-x^3+2x^2+2x-2)+(x^3+x^2-x-1)}{(x^5-x^3+2x^2-2)}\,$

$\frac{x^5+x^4+3x^2+x-3}{x^5-x^3+2x^2-2}\,$