Answer
$\frac{2x^2 + 38}{(x + 6)(x - 5)}$
Work Step by Step
To add or subtract rational expressions, we need to make sure that the expressions have the same denominator.
We need to rewrite the two expressions with the same denominator, so we need to find the least common denominator (LCD) of the two expressions.
The first thing we want to do is to make sure that each denominator is factored completely. This has already been done.
Next, we want to find the least common denominator (LCD). We do this by taking the highest power of each factor in the denominator:
LCD = $(x + 6)(x - 5)$
Now that we have the least common denominator, we multiply the numerator of each fraction with the factor or factors it is missing in its denominator:
$\frac{(x - 4)(x - 5)}{(x + 6)(x - 5)} + \frac{(x + 3)(x + 6)}{(x + 6)(x - 5)}$
Rewrite the two fractions as one with the same denominator:
$\frac{(x - 4)(x - 5) + (x + 3)(x + 6)}{(x + 6)(x - 5)}$
Use the distributive property to rewrite the numerator:
$\frac{(x^2 - 9x + 20) + (x^2 + 9x + 18)}{(x + 6)(x - 5)}$
Combine like terms in the numerator:
$\frac{2x^2 + 38}{(x + 6)(x - 5)}$
