Reduce the fraction $\frac{2}{6}$ to lowest terms by extracting and canceling out $2$.
$$4x-\frac{2}{y}+\frac{1}{3}$$
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $y$ and $3$ is $3y$. Multiply $\frac{2}{y}$ times $\frac{3}{3}$. Multiply $\frac{1}{3}$ times $\frac{y}{y}$.
$$4x-\frac{2\times 3}{3y}+\frac{y}{3y}$$
Since $-\frac{2\times 3}{3y}$ and $\frac{y}{3y}$ have the same denominator, add them by adding their numerators.
$$4x+\frac{-2\times 3+y}{3y}$$
Do the multiplications in $-2\times 3+y$.
$$4x+\frac{-6+y}{3y}$$
To add or subtract expressions, expand them to make their denominators the same. Multiply $4x$ times $\frac{3y}{3y}$.
$$\frac{4x\times 3y}{3y}+\frac{-6+y}{3y}$$
Since $\frac{4x\times 3y}{3y}$ and $\frac{-6+y}{3y}$ have the same denominator, add them by adding their numerators.
