Reduce the fraction $\frac{9}{15}$ to lowest terms by extracting and canceling out $3$.
$$\frac{3}{5}-\frac{4}{6}\times \frac{u}{6}$$
Reduce the fraction $\frac{4}{6}$ to lowest terms by extracting and canceling out $2$.
$$\frac{3}{5}-\frac{2}{3}\times \frac{u}{6}$$
Multiply $\frac{2}{3}$ times $\frac{u}{6}$ by multiplying numerator times numerator and denominator times denominator.
$$\frac{3}{5}-\frac{2u}{3\times 6}$$
Cancel out $2$ in both numerator and denominator.
$$\frac{3}{5}-\frac{u}{3\times 3}$$
Multiply $3$ and $3$ to get $9$.
$$\frac{3}{5}-\frac{u}{9}$$
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $5$ and $9$ is $45$. Multiply $\frac{3}{5}$ times $\frac{9}{9}$. Multiply $\frac{u}{9}$ times $\frac{5}{5}$.
$$\frac{3\times 9}{45}-\frac{5u}{45}$$
Since $\frac{3\times 9}{45}$ and $\frac{5u}{45}$ have the same denominator, subtract them by subtracting their numerators.
