Simplify (ab^2)/(ac)+(c^2b)/(ab)

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

Step 1

Simplify each term.

Cancel the common factor of $a$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $b$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

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

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

Step 3

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

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

Step 4

Write each expression with a common denominator of $c a$ , by multiplying each by an appropriate factor of $1$ .

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

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

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

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

Reorder the factors of $c a$ .

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

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

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

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

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

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

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

Add $2$ and $1$ .

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