Answer
$\displaystyle \frac{7x^{2}+12x-12}{(x-3)(x+2)(x+3)}$
Work Step by Step
1. Find the LCD .
1st denominator = $(x-3)(x+2)$
2nd denominator = $(x-3)(x+3)$
List factors of the 1st denominator.
From each next denominator, add only those factors that do not yet appear in the list.
LCD = $(x-3)(x+2)(x+3)$
2. Rewrite each rational expression with the the LCDas the denominator
= $\displaystyle \frac{(3x-2)(x+3)}{(x-3)(x+2)(x+3)}+\frac{(4x-3)(x+2)}{(x-3)(x+3)(x+2)}$
3. Add or subtract numerators, placing the resulting expression over the LCD.
= $\displaystyle \frac{(3x-2)(x+3)+(4x-3)(x+2)}{(x-3)(x+2)(x+3)}$
4. If possible, simplify.
= $\displaystyle \frac{3x^{2}+9x-2x-6+4x^{2}+8x-3x-6}{(x-3)(x+2)(x+3)} $
= $\displaystyle \frac{7x^{2}+12x-12}{(x-3)(x+2)(x+3)}$
The numerator has 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 $-84$ whose sum is $+12$
... we can't factor the numerator, so we leave it as is.
