To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $15$ and $5$ is $15$. Multiply $\frac{1}{5}$ times $\frac{3}{3}$.
$$\frac{4x}{15}-2x+\frac{3}{15}$$
Since $\frac{4x}{15}$ and $\frac{3}{15}$ have the same denominator, add them by adding their numerators.
$$\frac{4x+3}{15}-2x$$
To add or subtract expressions, expand them to make their denominators the same. Multiply $-2x$ times $\frac{15}{15}$.
$$\frac{4x+3}{15}+\frac{15\left(-2\right)x}{15}$$
Since $\frac{4x+3}{15}$ and $\frac{15\left(-2\right)x}{15}$ have the same denominator, add them by adding their numerators.
$$\frac{4x+3+15\left(-2\right)x}{15}$$
Do the multiplications in $4x+3+15\left(-2\right)x$.