How do you simplify the expression $\frac{x}{x + 1} + \frac{3}{x - 1}$ $x/(x+1) + 3/(x-1)$ ?

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How do you simplify the expression $\frac{x}{x + 1} + \frac{3}{x - 1}$ $x/(x+1) + 3/(x-1)$ ?

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Answer 1 · 2015-04-09T23:15:18

First you should make the denominators same;

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

$\frac{x \cdot (x - 1)}{(x + 1) \cdot (x - 1)} + \frac{3 \cdot (x + 1)}{(x + 1) \cdot (x - 1)}$ $(x * (x-1))/((x+1) * (x-1)) + (3*(x+1))/((x+1) * (x-1)$

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

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

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

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

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How do you simplify the expression $\frac{x}{x + 1} + \frac{3}{x - 1}$ $x/(x+1) + 3/(x-1)$ ?

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