Answer
$y = 1$
Work Step by Step
The least common denominator, or LCD, is $2y$.
Convert each fraction to an equivalent one by multiplying its numerator with whatever factor is missing between its denominator and the LCD:
$$\begin{align*}
\dfrac{2(2)}{2y} + \dfrac{1(y)}{2y} &= \dfrac{5}{2y}\\
\\\dfrac{4}{2y} + \dfrac{y}{2y} &= \dfrac{5}{2y}\\
\\\dfrac{4 + y}{2y} &= \dfrac{5}{2y}\\\end{align*}$$
Multiply each side of the equation by $2y$ to eliminate the fractions:
$$4 + y = 5$$
Subtract $4$ from each side of the equation to solve for $y$:
$$y = 1$$
To check the solution, plug in the value we just found for $y$ into the original equation:
$$\dfrac{2}{1} + \dfrac{1}{2} = \dfrac{5}{2(1)}$$
Simplify the fractions:
$$2 + \dfrac{1}{2} = \dfrac{5}{2}$$
Convert to equivalent fractions with $2$ as the LCD:
$$\dfrac{4}{2} + \dfrac{1}{2} = \dfrac{5}{2}$$
Add to simplify:
$$\frac{5}{2} = \frac{5}{2}$$
Both sides are equal to one another; therefore, this solution is correct.
