Simplify (3a)/(12b^2)-(a-4b)/(12b^2)

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

Step 1

Combine the numerators over the common denominator.

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

Step 2

Simplify each term.

Apply the distributive property.

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

Multiply $- 4$ by $- 1$ .

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

Step 3

Simplify terms.

Subtract $a$ from $3 a$ .

$\frac{2 a + 4 b}{12 b^{2}}$

Cancel the common factor of $2 a + 4 b$ and $12$ .

Factor $2$ out of $2 a$ .

$\frac{2 (a) + 4 b}{12 b^{2}}$

Factor $2$ out of $4 b$ .

$\frac{2 (a) + 2 (2 b)}{12 b^{2}}$

Factor $2$ out of $2 (a) + 2 (2 b)$ .

$\frac{2 (a + 2 b)}{12 b^{2}}$

Cancel the common factors.

Factor $2$ out of $12 b^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{a + 2 b}{6 b^{2}}$