Answer
$x = 1$
Work Step by Step
The least common denominator, or LCD, is $4$.
Multiply each side of the equation by $4$ to eliminate the fractions:
$$\begin{align*}
4 \cdot \frac{x}{2}&=\frac{x+1}{4} \cdot 4\\
\\2x &= x + 1
\end{align*}$$
Subtract $x$ from each side of the equation:
$$x = 1$$
To check the solution, plug in $1$ for $x$ into the original equation:
$$\begin{align*}
\frac{1}{2} &\stackrel{?}{=} \frac{1 + 1}{4}\\
\frac{1}{2}&\stackrel{?}{=}\frac{2}{4}\\
\frac{1}{2}&\stackrel{\checkmark}{=}\frac{1}{2}
\end{align*}$$
