Answer
$D$
Work Step by Step
Add the fractions in the numerator first. Find the least common denominator, LCD, which incorporates all factors in the denominators of the two fractions. Multiply the numerator in each fraction by the factor that is missing between its denominator and the LCD:
$\dfrac{\frac{1(y)}{xy} + \frac{3(x)}{xy}}{\frac{2}{xy}}$
Simplify:
$\dfrac{\frac{y}{xy} + \frac{3x}{xy}}{\frac{2}{xy}}$
Add the two fractions:
$\dfrac{\frac{3x + y}{xy}}{\frac{2}{xy}}$
Rewrite the exercise using the division ($\div$) symbol:
$\dfrac{3x + y}{xy} \div \dfrac{2}{xy}$
To divide one rational expression by another, multiply the first expression by the reciprocal of the second:
$\dfrac{3x + y}{xy} \cdot \dfrac{xy}{2}$
Cancel common factors in the numerator and denominator:
$\dfrac{3x + y}{2}$
This answer corresponds to option $D$.
