Question

the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer.
simplify: $\frac{3x^{2}}{x^{2}-25} - \frac{x}{x+5} + \frac{2}{x-5}$ , $x \
eq -5,5$
options:
$circ$ $\frac{2x^{2}+7x+5}{(x+5)(x-5)}$
$circ$ $\frac{2x^{2}-3x+10}{(x+5)(x-5)}$
$circ$ $\frac{2x^{2}+7x+10}{(x+5)(x-5)}$
$circ$ $\frac{2x^{2}-3x+5}{(x+5)(x-5)}$

Explanation:

Step1: Factor the denominator

Note that $x^2-25=(x+5)(x-5)$

Step2: Find common denominator

The common denominator is $(x+5)(x-5)$. Rewrite each term:
$\frac{3x^2}{(x+5)(x-5)} - \frac{x(x-5)}{(x+5)(x-5)} + \frac{2(x+5)}{(x+5)(x-5)}$

Step3: Expand numerator terms

$\frac{3x^2 - (x^2-5x) + (2x+10)}{(x+5)(x-5)}$

Step4: Simplify the numerator

$\frac{3x^2 -x^2 +5x +2x +10}{(x+5)(x-5)} = \frac{2x^2+7x+10}{(x+5)(x-5)}$

Answer:

$\frac{2x^2+7x+10}{(x+5)(x-5)}$ (corresponding to the second option)