$$\frac { 2 } { x + 1 } + \frac { 2 } { x - 1 } - \frac { x ^ { 2 } + 3 } { x ^ { 2 } - 1 }$$
Evaluate
$-\frac{x-3}{x+1}$
Short Solution Steps
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $x+1$ and $x-1$ is $\left(x-1\right)\left(x+1\right)$. Multiply $\frac{2}{x+1}$ times $\frac{x-1}{x-1}$. Multiply $\frac{2}{x-1}$ times $\frac{x+1}{x+1}$.
Since $\frac{2\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}$ and $\frac{2\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}$ have the same denominator, add them by adding their numerators.
Since $\frac{4x}{\left(x-1\right)\left(x+1\right)}$ and $\frac{x^{2}+3}{\left(x-1\right)\left(x+1\right)}$ have the same denominator, subtract them by subtracting their numerators.
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $x+1$ and $x-1$ is $\left(x-1\right)\left(x+1\right)$. Multiply $\frac{2}{x+1}$ times $\frac{x-1}{x-1}$. Multiply $\frac{2}{x-1}$ times $\frac{x+1}{x+1}$.
Since $\frac{2\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}$ and $\frac{2\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}$ have the same denominator, add them by adding their numerators.
Since $\frac{4x}{\left(x-1\right)\left(x+1\right)}$ and $\frac{x^{2}+3}{\left(x-1\right)\left(x+1\right)}$ have the same denominator, subtract them by subtracting their numerators.
