Simplify 5/(9z^3y)-1/(15z^2y)

$\frac{5}{9 z^{3} y} - \frac{1}{15 z^{2} y}$

Step 1

To write $\frac{5}{9 z^{3} y}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{5}{9 z^{3} y} \cdot \frac{5}{5} - \frac{1}{15 z^{2} y}$

Step 2

To write $- \frac{1}{15 z^{2} y}$ as a fraction with a common denominator, multiply by $\frac{3 z}{3 z}$ .

$\frac{5}{9 z^{3} y} \cdot \frac{5}{5} - \frac{1}{15 z^{2} y} \cdot \frac{3 z}{3 z}$

Step 3

Write each expression with a common denominator of $45 y z^{3}$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5}{9 z^{3} y}$ by $\frac{5}{5}$ .

$\frac{5 \cdot 5}{9 z^{3} y \cdot 5} - \frac{1}{15 z^{2} y} \cdot \frac{3 z}{3 z}$

Multiply $5$ by $9$ .

$\frac{5 \cdot 5}{45 z^{3} y} - \frac{1}{15 z^{2} y} \cdot \frac{3 z}{3 z}$

Multiply $\frac{1}{15 z^{2} y}$ by $\frac{3 z}{3 z}$ .

$\frac{5 \cdot 5}{45 z^{3} y} - \frac{3 z}{15 z^{2} y (3 z)}$

Multiply $3$ by $15$ .

$\frac{5 \cdot 5}{45 z^{3} y} - \frac{3 z}{45 z^{2} y z}$

Raise $z$ to the power of $1$ .

$\frac{5 \cdot 5}{45 z^{3} y} - \frac{3 z}{45 y (z^{2} z^{1})}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{5 \cdot 5}{45 z^{3} y} - \frac{3 z}{45 y z^{2 + 1}}$

Add $2$ and $1$ .

$\frac{5 \cdot 5}{45 z^{3} y} - \frac{3 z}{45 y z^{3}}$

Reorder the factors of $45 y z^{3}$ .

$\frac{5 \cdot 5}{45 z^{3} y} - \frac{3 z}{45 z^{3} y}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 \cdot 5 - 3 z}{45 z^{3} y}$

Step 5

Multiply $5$ by $5$ .

$\frac{25 - 3 z}{45 z^{3} y}$