Answer
$\displaystyle \frac{2x^{2}+10x+53}{(x+7)(x-2)}$
Work Step by Step
1. Find the LCD .
LCD = $(x+7)(x-2)$
2. Rewrite each rational expression with the the LCDas the denominator
= $\displaystyle \frac{(x-2)(x-2)}{(x+7)(x-2)}+\frac{(x+7)(x+7)}{(x+7)(x-2)}$
3. Add or subtract numerators, placing the resulting expression over the LCD.
= $\displaystyle \frac{(x-2)^{2}+(x+7)^{2}}{(x+7)(x-2)}$
4. If possible, simplify.
= $\displaystyle \frac{x^{2}-4x+4+x^{2}+14x+49}{(x+7)(x-2)} $
= $\displaystyle \frac{2x^{2}+10x+53}{(x+7)(x-2)}$
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 $106$ whose sum is $+10$
... we can't factor the numerator, so we leave it as it is.