Simplify 5/(6a^2)+1/(6ab)

$\frac{5}{6 a^{2}} + \frac{1}{6 a b}$

Step 1

To write $\frac{5}{6 a^{2}}$ as a fraction with a common denominator, multiply by $\frac{b}{b}$ .

$\frac{5}{6 a^{2}} \cdot \frac{b}{b} + \frac{1}{6 a b}$

Step 2

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

$\frac{5}{6 a^{2}} \cdot \frac{b}{b} + \frac{1}{6 a b} \cdot \frac{a}{a}$

Step 3

Write each expression with a common denominator of $6 b a^{2}$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5}{6 a^{2}}$ by $\frac{b}{b}$ .

$\frac{5 b}{6 a^{2} b} + \frac{1}{6 a b} \cdot \frac{a}{a}$

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

$\frac{5 b}{6 a^{2} b} + \frac{a}{6 a b a}$

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

$\frac{5 b}{6 a^{2} b} + \frac{a}{6 (a^{1} a) b}$

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

$\frac{5 b}{6 a^{2} b} + \frac{a}{6 (a^{1} a^{1}) b}$

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

$\frac{5 b}{6 a^{2} b} + \frac{a}{6 a^{1 + 1} b}$

Add $1$ and $1$ .

$\frac{5 b}{6 a^{2} b} + \frac{a}{6 a^{2} b}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 b + a}{6 a^{2} b}$