# How do you simplify the expression x/(x+1) + 3/(x-1)?

Apr 9, 2015

First you should make the denominators same;

$\frac{x}{x + 1} + \frac{3}{x - 1}$
so i will multiply the first term with $\frac{x - 1}{x - 1}$
and the second term with $\frac{x + 1}{x + 1}$;

(x * (x-1))/((x+1) * (x-1)) + (3*(x+1))/((x+1) * (x-1)

$= \frac{{x}^{2} - x + 3 x + 3}{\left(x - 1\right) \cdot \left(x + 1\right)}$

= $\frac{{x}^{2} + 2 x + 3}{\left(x - 1\right) \cdot \left(x + 1\right)}$

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

I can only get this far. I don't know if there is a more simplest result. I hope it helps.