Pre-Algebra Examples

$(p^{3} q r^{2} + p^{2} q^{2} r^{3} - p^{5} q^{3} r^{2}) \div p^{2} q r^{2}$

Step 1

Rewrite the division as a fraction.

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

Factor $p^{2} q r^{2}$ out of $p^{2} q r^{2} (p) + p^{2} q r^{2} (q r)$ .

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

Step 2.5

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

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

Step 3

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

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

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

Step 4

Cancel the common factor of $q$ .

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Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

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

Step 5

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

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Step 5.1

Cancel the common factor.

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

Step 5.2

Divide $p + q r - p^{3} q^{2}$ by $1$ .

$p + q r - p^{3} q^{2}$