Answer
$\text{C}$
Work Step by Step
To subtract two rational expressions, make sure that the denominators are the same, meaning we need to find the least common denominator, or LCD.
First, factor the numerators and the denominators:
$\dfrac{5x}{(x - 3)(x + 3)} - \dfrac{4x}{(x + 3)(x + 2)}$
Before subtracting the two rational expressions, find the LCD. The LCD is the product of all factors found in the denominators of both rational expressions.
After finding the LCD, multiply each numerator by the factor in the common denominator that is missing:
$\dfrac{(5x)(x + 2)}{(x - 3)(x + 3)(x + 2)}- \dfrac{(4x)(x - 3)}{(x + 3)(x + 2)(x - 3)}$
Expand the binomials using the distribute property, and then multiply to simplify:
$\dfrac{5x^2 + 10x }{(x - 3)(x + 3)(x + 2)}-\dfrac{4x^2 - 12x}{(x - 3)(x + 3)(x + 2)}=\dfrac{5x^2 + 10x - 4x^2 + 12x}{(x - 3)(x + 3)(x + 2)}$
Simplify by combining like terms:
$\dfrac{x^2 + 22x}{(x - 3)(x + 3)(x + 2)}$
This answer corresponds to option $C$.
