Divide (28p^3q^2r-36p^2r^2+16q^5r^4)/(4pq^2r)

$\frac{28 p^{3} q^{2} r - 36 p^{2} r^{2} + 16 q^{5} r^{4}}{4 p q^{2} r}$

Step 1

Factor $4 r$ out of $28 p^{3} q^{2} r - 36 p^{2} r^{2} + 16 q^{5} r^{4}$ .

Factor $4 r$ out of $28 p^{3} q^{2} r$ .

$\frac{4 r (7 p^{3} q^{2}) - 36 p^{2} r^{2} + 16 q^{5} r^{4}}{4 p q^{2} r}$

Factor $4 r$ out of $- 36 p^{2} r^{2}$ .

$\frac{4 r (7 p^{3} q^{2}) + 4 r (- 9 p^{2} r) + 16 q^{5} r^{4}}{4 p q^{2} r}$

Factor $4 r$ out of $16 q^{5} r^{4}$ .

$\frac{4 r (7 p^{3} q^{2}) + 4 r (- 9 p^{2} r) + 4 r (4 q^{5} r^{3})}{4 p q^{2} r}$

Factor $4 r$ out of $4 r (7 p^{3} q^{2}) + 4 r (- 9 p^{2} r)$ .

$\frac{4 r (7 p^{3} q^{2} - 9 p^{2} r) + 4 r (4 q^{5} r^{3})}{4 p q^{2} r}$

Factor $4 r$ out of $4 r (7 p^{3} q^{2} - 9 p^{2} r) + 4 r (4 q^{5} r^{3})$ .

$\frac{4 r (7 p^{3} q^{2} - 9 p^{2} r + 4 q^{5} r^{3})}{4 p q^{2} r}$

Step 2

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 r (7 p^{3} q^{2} - 9 p^{2} r + 4 q^{5} r^{3})}{4 p q^{2} r}$

Rewrite the expression.

$\frac{r (7 p^{3} q^{2} - 9 p^{2} r + 4 q^{5} r^{3})}{p q^{2} r}$

Step 3

Cancel the common factor of $r$ .

Cancel the common factor.

$\frac{r (7 p^{3} q^{2} - 9 p^{2} r + 4 q^{5} r^{3})}{p q^{2} r}$

Rewrite the expression.

$\frac{7 p^{3} q^{2} - 9 p^{2} r + 4 q^{5} r^{3}}{p q^{2}}$

Step 4

Split the fraction $\frac{7 p^{3} q^{2} - 9 p^{2} r + 4 q^{5} r^{3}}{p q^{2}}$ into two fractions.

$\frac{7 p^{3} q^{2} - 9 p^{2} r}{p q^{2}} + \frac{4 q^{5} r^{3}}{p q^{2}}$

Step 5

Split the fraction $\frac{7 p^{3} q^{2} - 9 p^{2} r}{p q^{2}}$ into two fractions.

$\frac{7 p^{3} q^{2}}{p q^{2}} + \frac{- 9 p^{2} r}{p q^{2}} + \frac{4 q^{5} r^{3}}{p q^{2}}$

Step 6

Cancel the common factor of $p^{3}$ and $p$ .

Factor $p$ out of $7 p^{3} q^{2}$ .

$\frac{p (7 p^{2} q^{2})}{p q^{2}} + \frac{- 9 p^{2} r}{p q^{2}} + \frac{4 q^{5} r^{3}}{p q^{2}}$

Cancel the common factors.

Factor $p$ out of $p q^{2}$ .

$\frac{p (7 p^{2} q^{2})}{p (q^{2})} + \frac{- 9 p^{2} r}{p q^{2}} + \frac{4 q^{5} r^{3}}{p q^{2}}$

Cancel the common factor.

$\frac{p (7 p^{2} q^{2})}{p q^{2}} + \frac{- 9 p^{2} r}{p q^{2}} + \frac{4 q^{5} r^{3}}{p q^{2}}$

Rewrite the expression.

$\frac{7 p^{2} q^{2}}{q^{2}} + \frac{- 9 p^{2} r}{p q^{2}} + \frac{4 q^{5} r^{3}}{p q^{2}}$

Step 7

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

Cancel the common factor.

$\frac{7 p^{2} q^{2}}{q^{2}} + \frac{- 9 p^{2} r}{p q^{2}} + \frac{4 q^{5} r^{3}}{p q^{2}}$

Divide $7 p^{2}$ by $1$ .

$7 p^{2} + \frac{- 9 p^{2} r}{p q^{2}} + \frac{4 q^{5} r^{3}}{p q^{2}}$

Step 8

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

Factor $p$ out of $- 9 p^{2} r$ .

$7 p^{2} + \frac{p (- 9 p r)}{p q^{2}} + \frac{4 q^{5} r^{3}}{p q^{2}}$

Cancel the common factors.

Factor $p$ out of $p q^{2}$ .

$7 p^{2} + \frac{p (- 9 p r)}{p (q^{2})} + \frac{4 q^{5} r^{3}}{p q^{2}}$

Cancel the common factor.

$7 p^{2} + \frac{p (- 9 p r)}{p q^{2}} + \frac{4 q^{5} r^{3}}{p q^{2}}$

Rewrite the expression.

$7 p^{2} + \frac{- 9 p r}{q^{2}} + \frac{4 q^{5} r^{3}}{p q^{2}}$

Step 9

Move the negative in front of the fraction.

$7 p^{2} - \frac{9 p r}{q^{2}} + \frac{4 q^{5} r^{3}}{p q^{2}}$

Step 10

Cancel the common factor of $q^{5}$ and $q^{2}$ .

Factor $q^{2}$ out of $4 q^{5} r^{3}$ .

$7 p^{2} - \frac{9 p r}{q^{2}} + \frac{q^{2} (4 q^{3} r^{3})}{p q^{2}}$

Cancel the common factors.

Factor $q^{2}$ out of $p q^{2}$ .

$7 p^{2} - \frac{9 p r}{q^{2}} + \frac{q^{2} (4 q^{3} r^{3})}{q^{2} p}$

Cancel the common factor.

$7 p^{2} - \frac{9 p r}{q^{2}} + \frac{q^{2} (4 q^{3} r^{3})}{q^{2} p}$

Rewrite the expression.

$7 p^{2} - \frac{9 p r}{q^{2}} + \frac{4 q^{3} r^{3}}{p}$

Divide (28p^3q^2r-36p^2r^2+16q^5r^4)/(4pq^2r)

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