Simplify 1/(6a)-3/(4a^2)

$\frac{1}{6 a} - \frac{3}{4 a^{2}}$

To write $\frac{1}{6 a}$ as a fraction with a common denominator, multiply by $\frac{2 a}{2 a}$ .

$\frac{1}{6 a} \cdot \frac{2 a}{2 a} - \frac{3}{4 a^{2}}$

To write $- \frac{3}{4 a^{2}}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{1}{6 a} \cdot \frac{2 a}{2 a} - \frac{3}{4 a^{2}} \cdot \frac{3}{3}$

Write each expression with a common denominator of $12 a^{2}$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{6 a}$ by $\frac{2 a}{2 a}$ .

$\frac{2 a}{6 a (2 a)} - \frac{3}{4 a^{2}} \cdot \frac{3}{3}$

Multiply $2$ by $6$ .

$\frac{2 a}{12 a \cdot a} - \frac{3}{4 a^{2}} \cdot \frac{3}{3}$

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

$\frac{2 a}{12 (a^{1} a)} - \frac{3}{4 a^{2}} \cdot \frac{3}{3}$

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

$\frac{2 a}{12 (a^{1} a^{1})} - \frac{3}{4 a^{2}} \cdot \frac{3}{3}$

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

$\frac{2 a}{12 a^{1 + 1}} - \frac{3}{4 a^{2}} \cdot \frac{3}{3}$

Add $1$ and $1$ .

$\frac{2 a}{12 a^{2}} - \frac{3}{4 a^{2}} \cdot \frac{3}{3}$

Multiply $\frac{3}{4 a^{2}}$ by $\frac{3}{3}$ .

$\frac{2 a}{12 a^{2}} - \frac{3 \cdot 3}{4 a^{2} \cdot 3}$

Multiply $3$ by $4$ .

$\frac{2 a}{12 a^{2}} - \frac{3 \cdot 3}{12 a^{2}}$

Combine the numerators over the common denominator.

$\frac{2 a - 3 \cdot 3}{12 a^{2}}$

Multiply $- 3$ by $3$ .

$\frac{2 a - 9}{12 a^{2}}$