Answer
$C$
Work Step by Step
Factor all expressions to their simplest forms:
$\dfrac{5x}{(x - 3)(x + 3)} - \dfrac{4x}{(x + 3)(x + 2)}$
The least common denominator, or LCD, incorporates all factors in the denominators of the fractions. In this case, the LCD is $(x - 3)(x + 3)(x + 2)$.
Convert each fraction to an equivalent one by multiplying its numerator with whatever factor is missing between its denominator and the LCD:
$\dfrac{5x(x + 2)}{(x - 3)(x + 3)(x + 2)} - \dfrac{4x(x - 3)}{(x - 3)(x + 3)(x + 2)}$
Multiply to simplify:
$\dfrac{5x^2 + 10x}{(x - 3)(x + 3)(x + 2)} - \dfrac{4x^2 - 12x}{(x - 3)(x + 3)(x + 2)}$
Subtract the fractions:
$$\begin{align*}
\dfrac{5x^2+10x-(4x^2-12x)}{(x-3)(x+3)(x+2)}&=\dfrac{5x^2+10x-4x^2+12x}{(x-3)(x+3)(x+2)}\\
&=\dfrac{x^2 + 22x}{(x - 3)(x + 3)(x + 2)}
\end{align*}$$
This answer corresponds to option $C$.
