Answer
$\displaystyle \frac{x^{2}+x+4}{(x-6)(x-1)(x+1)}$
Work Step by Step
1. Find the LCD .
1st denominator = $(x-6)(x-1)$
2nd denominator = $(x-6)(x+1)$
List factors of the 1st denominator.
From each next denominator, add only those factors that do not yet appear in the list.
LCD = $(x-6)(x-1)(x+1)$
2. Rewrite each rational expression with the the LCDas the denominator
= $\displaystyle \frac{(2x+1)(x+1)}{(x-6)(x-1)(x+1)}-\frac{(x+3)(x-1)}{ (x-6)(x+1)(x-1)}$
3. Add or subtract numerators, placing the resulting expression over the LCD.
= $\displaystyle \frac{(2x+1)(x+1)-(x+3)(x-1)}{(x-6)(x-1)(x+1)}$
4. If possible, simplify.
= $\displaystyle \frac{2x^{2}+2x+x+1-(x^{2}+3x-x-3)}{(x-6)(x-1)(x+1)} $
= $\displaystyle \frac{2x^{2}+2x+x+1-x^{2}-3x+x+3}{(x-6)(x-1)(x+1)} $
= $\displaystyle \frac{x^{2}+x+4}{(x-6)(x-1)(x+1)}$
