Divide (60a^2b^3-48b^4+84a^5b^2)/(12ab^2)

$\frac{60 a^{2} b^{3} - 48 b^{4} + 84 a^{5} b^{2}}{12 a b^{2}}$

Step 1

Factor $12 b^{2}$ out of $60 a^{2} b^{3} - 48 b^{4} + 84 a^{5} b^{2}$ .

Factor $12 b^{2}$ out of $60 a^{2} b^{3}$ .

$\frac{12 b^{2} (5 a^{2} b) - 48 b^{4} + 84 a^{5} b^{2}}{12 a b^{2}}$

Factor $12 b^{2}$ out of $- 48 b^{4}$ .

$\frac{12 b^{2} (5 a^{2} b) + 12 b^{2} (- 4 b^{2}) + 84 a^{5} b^{2}}{12 a b^{2}}$

Factor $12 b^{2}$ out of $84 a^{5} b^{2}$ .

$\frac{12 b^{2} (5 a^{2} b) + 12 b^{2} (- 4 b^{2}) + 12 b^{2} (7 a^{5})}{12 a b^{2}}$

Factor $12 b^{2}$ out of $12 b^{2} (5 a^{2} b) + 12 b^{2} (- 4 b^{2})$ .

$\frac{12 b^{2} (5 a^{2} b - 4 b^{2}) + 12 b^{2} (7 a^{5})}{12 a b^{2}}$

Factor $12 b^{2}$ out of $12 b^{2} (5 a^{2} b - 4 b^{2}) + 12 b^{2} (7 a^{5})$ .

$\frac{12 b^{2} (5 a^{2} b - 4 b^{2} + 7 a^{5})}{12 a b^{2}}$

Step 2

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{12 b^{2} (5 a^{2} b - 4 b^{2} + 7 a^{5})}{12 a b^{2}}$

Rewrite the expression.

$\frac{b^{2} (5 a^{2} b - 4 b^{2} + 7 a^{5})}{a b^{2}}$

Step 3

Cancel the common factor of $b^{2}$ .

Cancel the common factor.

$\frac{b^{2} (5 a^{2} b - 4 b^{2} + 7 a^{5})}{a b^{2}}$

Rewrite the expression.

$\frac{5 a^{2} b - 4 b^{2} + 7 a^{5}}{a}$

Step 4

Split the fraction $\frac{5 a^{2} b - 4 b^{2} + 7 a^{5}}{a}$ into two fractions.

$\frac{5 a^{2} b - 4 b^{2}}{a} + \frac{7 a^{5}}{a}$

Step 5

Split the fraction $\frac{5 a^{2} b - 4 b^{2}}{a}$ into two fractions.

$\frac{5 a^{2} b}{a} + \frac{- 4 b^{2}}{a} + \frac{7 a^{5}}{a}$

Step 6

Cancel the common factor of $a^{2}$ and $a$ .

Factor $a$ out of $5 a^{2} b$ .

$\frac{a (5 a b)}{a} + \frac{- 4 b^{2}}{a} + \frac{7 a^{5}}{a}$

Cancel the common factors.

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

$\frac{a (5 a b)}{a^{1}} + \frac{- 4 b^{2}}{a} + \frac{7 a^{5}}{a}$

Factor $a$ out of $a^{1}$ .

$\frac{a (5 a b)}{a \cdot 1} + \frac{- 4 b^{2}}{a} + \frac{7 a^{5}}{a}$

Cancel the common factor.

$\frac{a (5 a b)}{a \cdot 1} + \frac{- 4 b^{2}}{a} + \frac{7 a^{5}}{a}$

Rewrite the expression.

$\frac{5 a b}{1} + \frac{- 4 b^{2}}{a} + \frac{7 a^{5}}{a}$

Divide $5 a b$ by $1$ .

$5 a b + \frac{- 4 b^{2}}{a} + \frac{7 a^{5}}{a}$

Step 7

Move the negative in front of the fraction.

$5 a b - \frac{4 b^{2}}{a} + \frac{7 a^{5}}{a}$

Step 8

Cancel the common factor of $a^{5}$ and $a$ .

Factor $a$ out of $7 a^{5}$ .

$5 a b - \frac{4 b^{2}}{a} + \frac{a (7 a^{4})}{a}$

Cancel the common factors.

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

$5 a b - \frac{4 b^{2}}{a} + \frac{a (7 a^{4})}{a^{1}}$

Factor $a$ out of $a^{1}$ .

$5 a b - \frac{4 b^{2}}{a} + \frac{a (7 a^{4})}{a \cdot 1}$

Cancel the common factor.

$5 a b - \frac{4 b^{2}}{a} + \frac{a (7 a^{4})}{a \cdot 1}$

Rewrite the expression.

$5 a b - \frac{4 b^{2}}{a} + \frac{7 a^{4}}{1}$

Divide $7 a^{4}$ by $1$ .

$5 a b - \frac{4 b^{2}}{a} + 7 a^{4}$

Divide (60a^2b^3-48b^4+84a^5b^2)/(12ab^2)

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