$$\frac{3x}{3x}+\frac{x-3y}{3x}-\frac{5x-6y}{9x}$$
Since $\frac{3x}{3x}$ and $\frac{x-3y}{3x}$ have the same denominator, add them by adding their numerators.$$\frac{3x+x-3y}{3x}-\frac{5x-6y}{9x}$$
Combine like terms in $3x+x-3y$.$$\frac{4x-3y}{3x}-\frac{5x-6y}{9x}$$
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $3x$ and $9x$ is $9x$. Multiply $\frac{4x-3y}{3x}$ times $\frac{3}{3}$.$$\frac{3\left(4x-3y\right)}{9x}-\frac{5x-6y}{9x}$$
Since $\frac{3\left(4x-3y\right)}{9x}$ and $\frac{5x-6y}{9x}$ have the same denominator, subtract them by subtracting their numerators.$$\frac{3\left(4x-3y\right)-\left(5x-6y\right)}{9x}$$
Do the multiplications in $3\left(4x-3y\right)-\left(5x-6y\right)$.$$\frac{12x-9y-5x+6y}{9x}$$
Combine like terms in $12x-9y-5x+6y$.$$\frac{7x-3y}{9x}$$