Answer
$y = 2$
Work Step by Step
Before we can solve the equation, find the least common denominator for the two fractions. The least common denominator, or LCD, is $3(y + 1)$, in this case.
Convert each fraction to an equivalent one by multiplying its numerator with whatever factor is missing between its denominator and the LCD:
$\dfrac{y(3)}{3(y + 1)} = \dfrac{2(y + 1)}{3(y + 1)}$
Distribute and multiply to simplify:
$\dfrac{3y}{3(y + 1)} = \dfrac{2y + 2}{3(y + 1)}$
Multiply both sides of the equation by $3(y + 1)$ to eliminate the fractions:
$3y = 2y + 2$
Subtract $2y$ from each side of the equation:
$y = 2$
To check the solution, plug in $2$ for $y$ into the original equation:
$\dfrac{2}{2 + 1} = \dfrac{2}{3}$
Simplify:
$\frac{2}{3} = \frac{2}{3}$
Both sides are equal to one another; therefore, this solution is correct.
