Simplify 2/(a^3b^3)-1/(a^2b^3)

$\frac{2}{a^{3} b^{3}} - \frac{1}{a^{2} b^{3}}$

Step 1

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

$\frac{2}{a^{3} b^{3}} - \frac{1}{a^{2} b^{3}} \cdot \frac{a}{a}$

Step 2

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

Multiply $\frac{1}{a^{2} b^{3}}$ by $\frac{a}{a}$ .

$\frac{2}{a^{3} b^{3}} - \frac{a}{a^{2} b^{3} a}$

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

$\frac{2}{a^{3} b^{3}} - \frac{a}{a^{1} a^{2} b^{3}}$

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

$\frac{2}{a^{3} b^{3}} - \frac{a}{a^{1 + 2} b^{3}}$

Add $1$ and $2$ .

$\frac{2}{a^{3} b^{3}} - \frac{a}{a^{3} b^{3}}$

Step 3

Combine the numerators over the common denominator.

$\frac{2 - a}{a^{3} b^{3}}$