Simplify 1/(6c^2d)+3/(4cd^3)

$\frac{1}{6 c^{2} d} + \frac{3}{4 c d^{3}}$

Step 1

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

$\frac{1}{6 c^{2} d} \cdot \frac{2 d^{2}}{2 d^{2}} + \frac{3}{4 c d^{3}}$

Step 2

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

$\frac{1}{6 c^{2} d} \cdot \frac{2 d^{2}}{2 d^{2}} + \frac{3}{4 c d^{3}} \cdot \frac{3 c}{3 c}$

Step 3

Write each expression with a common denominator of $12 c^{2} d^{3}$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{6 c^{2} d}$ by $\frac{2 d^{2}}{2 d^{2}}$ .

$\frac{2 d^{2}}{6 c^{2} d (2 d^{2})} + \frac{3}{4 c d^{3}} \cdot \frac{3 c}{3 c}$

Multiply $2$ by $6$ .

$\frac{2 d^{2}}{12 c^{2} d \cdot d^{2}} + \frac{3}{4 c d^{3}} \cdot \frac{3 c}{3 c}$

Multiply $d$ by $d^{2}$ by adding the exponents.

Move $d^{2}$ .

$\frac{2 d^{2}}{12 c^{2} (d^{2} d)} + \frac{3}{4 c d^{3}} \cdot \frac{3 c}{3 c}$

Multiply $d^{2}$ by $d$ .

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

$\frac{2 d^{2}}{12 c^{2} (d^{2} d^{1})} + \frac{3}{4 c d^{3}} \cdot \frac{3 c}{3 c}$

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

$\frac{2 d^{2}}{12 c^{2} d^{2 + 1}} + \frac{3}{4 c d^{3}} \cdot \frac{3 c}{3 c}$

Add $2$ and $1$ .

$\frac{2 d^{2}}{12 c^{2} d^{3}} + \frac{3}{4 c d^{3}} \cdot \frac{3 c}{3 c}$

Multiply $\frac{3}{4 c d^{3}}$ by $\frac{3 c}{3 c}$ .

$\frac{2 d^{2}}{12 c^{2} d^{3}} + \frac{3 (3 c)}{4 c d^{3} (3 c)}$

Multiply $3$ by $4$ .

$\frac{2 d^{2}}{12 c^{2} d^{3}} + \frac{3 (3 c)}{12 c d^{3} c}$

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

$\frac{2 d^{2}}{12 c^{2} d^{3}} + \frac{3 (3 c)}{12 (c^{1} c) d^{3}}$

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

$\frac{2 d^{2}}{12 c^{2} d^{3}} + \frac{3 (3 c)}{12 (c^{1} c^{1}) d^{3}}$

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

$\frac{2 d^{2}}{12 c^{2} d^{3}} + \frac{3 (3 c)}{12 c^{1 + 1} d^{3}}$

Add $1$ and $1$ .

$\frac{2 d^{2}}{12 c^{2} d^{3}} + \frac{3 (3 c)}{12 c^{2} d^{3}}$

Step 4

Combine the numerators over the common denominator.

$\frac{2 d^{2} + 3 (3 c)}{12 c^{2} d^{3}}$

Step 5

Multiply $3$ by $3$ .

$\frac{2 d^{2} + 9 c}{12 c^{2} d^{3}}$