$$( \frac { x + 2 } { x - 2 } - \frac { x } { x + 2 } ) \frac { x - 2 } { 33 + 2 } =$$
Evaluate
$\frac{2\left(3x+2\right)}{35\left(x+2\right)}$
Short Solution Steps
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $x-2$ and $x+2$ is $\left(x-2\right)\left(x+2\right)$. Multiply $\frac{x+2}{x-2}$ times $\frac{x+2}{x+2}$. Multiply $\frac{x}{x+2}$ times $\frac{x-2}{x-2}$.
Since $\frac{\left(x+2\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}$ and $\frac{x\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}$ have the same denominator, subtract them by subtracting their numerators.
Multiply $\frac{6x+4}{\left(x-2\right)\left(x+2\right)}$ times $\frac{x-2}{35}$ by multiplying numerator times numerator and denominator times denominator.
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $x-2$ and $x+2$ is $\left(x-2\right)\left(x+2\right)$. Multiply $\frac{x+2}{x-2}$ times $\frac{x+2}{x+2}$. Multiply $\frac{x}{x+2}$ times $\frac{x-2}{x-2}$.
Since $\frac{\left(x+2\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}$ and $\frac{x\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}$ have the same denominator, subtract them by subtracting their numerators.
Multiply $\frac{6x+4}{\left(x-2\right)\left(x+2\right)}$ times $\frac{x-2}{35}$ by multiplying numerator times numerator and denominator times denominator.
