Simplify (3b)/2-(4a)/(6a^2b)

$\frac{3 b}{2} - \frac{4 a}{6 a^{2} b}$

Simplify each term.

Cancel the common factor of $4$ and $6$ .

Factor $2$ out of $4 a$ .

$\frac{3 b}{2} - \frac{2 (2 a)}{6 a^{2} b}$

Cancel the common factors.

Factor $2$ out of $6 a^{2} b$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $a$ and $a^{2}$ .

Factor $a$ out of $2 a$ .

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

Cancel the common factors.

Factor $a$ out of $3 a^{2} b$ .

$\frac{3 b}{2} - \frac{a \cdot 2}{a (3 a b)}$

Cancel the common factor.

$\frac{3 b}{2} - \frac{a \cdot 2}{a (3 a b)}$

Rewrite the expression.

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

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

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

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

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

Write each expression with a common denominator of $6 a b$ , by multiplying each by an appropriate factor of $1$ .

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

$\frac{3 b (3 a b)}{2 (3 a b)} - \frac{2}{3 a b} \cdot \frac{2}{2}$

Multiply $3$ by $2$ .

$\frac{3 b (3 a b)}{6 (a b)} - \frac{2}{3 a b} \cdot \frac{2}{2}$

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

$\frac{3 b (3 a b)}{6 (a b)} - \frac{2 \cdot 2}{3 a b \cdot 2}$

Multiply $2$ by $3$ .

$\frac{3 b (3 a b)}{6 (a b)} - \frac{2 \cdot 2}{6 a b}$

Reorder the factors of $6 (a b)$ .

$\frac{3 b (3 a b)}{6 a b} - \frac{2 \cdot 2}{6 a b}$

Combine the numerators over the common denominator.

$\frac{3 b (3 a b) - 2 \cdot 2}{6 a b}$

Simplify the numerator.

Multiply $b$ by $b$ by adding the exponents.

Move $b$ .

$\frac{3 (b \cdot b) (3 a) - 2 \cdot 2}{6 a b}$

Multiply $b$ by $b$ .

$\frac{3 b^{2} (3 a) - 2 \cdot 2}{6 a b}$

Rewrite using the commutative property of multiplication.

$\frac{3 \cdot 3 b^{2} a - 2 \cdot 2}{6 a b}$

Multiply $3$ by $3$ .

$\frac{9 b^{2} a - 2 \cdot 2}{6 a b}$

Multiply $- 2$ by $2$ .

$\frac{9 b^{2} a - 4}{6 a b}$

Simplify (3b)/2-(4a)/(6a^2b)

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