Simplify 1/(b^2c)+b/(c^2)

$\frac{1}{b^{2} c} + \frac{b}{c^{2}}$

Step 1

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

$\frac{1}{b^{2} c} \cdot \frac{c}{c} + \frac{b}{c^{2}}$

Step 2

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

$\frac{1}{b^{2} c} \cdot \frac{c}{c} + \frac{b}{c^{2}} \cdot \frac{b^{2}}{b^{2}}$

Step 3

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

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

$\frac{c}{b^{2} c \cdot c} + \frac{b}{c^{2}} \cdot \frac{b^{2}}{b^{2}}$

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

$\frac{c}{b^{2} (c^{1} c)} + \frac{b}{c^{2}} \cdot \frac{b^{2}}{b^{2}}$

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

$\frac{c}{b^{2} (c^{1} c^{1})} + \frac{b}{c^{2}} \cdot \frac{b^{2}}{b^{2}}$

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

$\frac{c}{b^{2} c^{1 + 1}} + \frac{b}{c^{2}} \cdot \frac{b^{2}}{b^{2}}$

Add $1$ and $1$ .

$\frac{c}{b^{2} c^{2}} + \frac{b}{c^{2}} \cdot \frac{b^{2}}{b^{2}}$

Multiply $\frac{b}{c^{2}}$ by $\frac{b^{2}}{b^{2}}$ .

$\frac{c}{b^{2} c^{2}} + \frac{b \cdot b^{2}}{c^{2} b^{2}}$

Reorder the factors of $c^{2} b^{2}$ .

$\frac{c}{b^{2} c^{2}} + \frac{b \cdot b^{2}}{b^{2} c^{2}}$

Step 4

Combine the numerators over the common denominator.

$\frac{c + b \cdot b^{2}}{b^{2} c^{2}}$

Step 5

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

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

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

$\frac{c + b^{1} b^{2}}{b^{2} c^{2}}$

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

$\frac{c + b^{1 + 2}}{b^{2} c^{2}}$

Add $1$ and $2$ .

$\frac{c + b^{3}}{b^{2} c^{2}}$