Answer
$\displaystyle \frac{2x^{2}-2x+61}{(x+5)(x-6)}$
Work Step by Step
1. Find the LCD .
LCD = $(x+5)(x-6)$
2. Rewrite each rational expression with the the LCD as the denominator
= $\displaystyle \frac{(x-6)(x-6)}{(x+5)(x-6)}+\frac{(x+5)(x+5)}{(x-6)(x+5)}$
3. Add or subtract numerators, placing the resulting expression over the LCD.
= $\displaystyle \frac{(x-6)^{2}+(x+5)^{2}}{(x+5)(x-6)}$
4. If possible, simplify.
= $\displaystyle \frac{x^{2}-12x+36+x^{2}+10x+25}{(x+5)(x-6)} $
= $\displaystyle \frac{2x^{2}-2x+61}{(x+5)(x-6)}$
The numerator is of the form $ax^{2}+bx+c.$
To factor, find factors of $ac$ whose sum is $b.$
If successful, rewrite $bx$ and factor in pairs.
... we can't find factors of $122$ whose sum is $-2$
... we can't factor the numerator, so we leave it as it is.
