1. ## simplify

simplify

I) $\displaystyle \frac{x}{x-1}+\frac{x+2}{x^2-1}$

2. Originally Posted by william
simplify

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

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

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

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

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

3. Originally Posted by Mush
$\displaystyle \frac{x}{x-1}+\frac{x+2}{(x-1)(x+1)}$

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

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

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

$\displaystyle \frac{x^2+2x+ 2}{(x+1)(x-1)}$
very nicely done thanks

4. Originally Posted by Mush
$\displaystyle \frac{x}{x-1}+\frac{x+2}{(x-1)(x+1)}$

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

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

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

$\displaystyle \frac{x^2+2x+ 2}{(x+1)(x-1)}$
what would change if it was I) $\displaystyle \frac{x}{x-1}+\frac{x+1}{x^2-1}$