Evaluate: -y/(3x)+7/9

Evaluate: $-\frac{y}{3x}+\frac{7}{9}$

To add or subtract expressions, expand them to make their denominators the same. Multiply $1$ times $\frac{3x}{3x}$.

$$\frac{3x}{3x}+\frac{x-3y}{3x}-\frac{5x-6y}{9x}$$

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 $12x-9y-5x+6y$.

$$\frac{7x-3y}{9x}$$