Pre-Algebra Examples

$(9 x^{5} v^{4} - 6 x v^{4}) \div 3 x^{4 v^{3}}$

Step 1

Rewrite the division as a fraction.

$\frac{9 x^{5} v^{4} - 6 x v^{4}}{3 x^{4 v^{3}}}$

Step 2

Factor $3 x v^{4}$ out of $9 x^{5} v^{4} - 6 x v^{4}$ .

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Step 2.1

Factor $3 x v^{4}$ out of $9 x^{5} v^{4}$ .

$\frac{3 x v^{4} (3 x^{4}) - 6 x v^{4}}{3 x^{4 v^{3}}}$

Step 2.2

Factor $3 x v^{4}$ out of $- 6 x v^{4}$ .

$\frac{3 x v^{4} (3 x^{4}) + 3 x v^{4} (- 2)}{3 x^{4 v^{3}}}$

Step 2.3

Factor $3 x v^{4}$ out of $3 x v^{4} (3 x^{4}) + 3 x v^{4} (- 2)$ .

$\frac{3 x v^{4} (3 x^{4} - 2)}{3 x^{4 v^{3}}}$

Step 3

Cancel the common factor of $3$ .

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Step 3.1

Cancel the common factor.

$\frac{3 x v^{4} (3 x^{4} - 2)}{3 x^{4 v^{3}}}$

Step 3.2

Rewrite the expression.

$\frac{x v^{4} (3 x^{4} - 2)}{x^{4 v^{3}}}$

Step 4

Apply the distributive property.

$\frac{x v^{4} (3 x^{4}) + x v^{4} \cdot - 2}{x^{4 v^{3}}}$

Step 5

Rewrite using the commutative property of multiplication.

$\frac{3 x v^{4} x^{4} + x v^{4} \cdot - 2}{x^{4 v^{3}}}$

Step 6

Move $- 2$ to the left of $x v^{4}$ .

$\frac{3 x v^{4} x^{4} - 2 \cdot (x v^{4})}{x^{4 v^{3}}}$

Step 7

Multiply $x$ by $x^{4}$ by adding the exponents.

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Step 7.1

Move $x^{4}$ .

$\frac{3 (x^{4} x) v^{4} - 2 \cdot (x v^{4})}{x^{4 v^{3}}}$

Step 7.2

Multiply $x^{4}$ by $x$ .

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Step 7.2.1

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

$\frac{3 (x^{4} x^{1}) v^{4} - 2 \cdot (x v^{4})}{x^{4 v^{3}}}$

Step 7.2.2

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

$\frac{3 x^{4 + 1} v^{4} - 2 \cdot (x v^{4})}{x^{4 v^{3}}}$

Step 7.3

Add $4$ and $1$ .

$\frac{3 x^{5} v^{4} - 2 \cdot (x v^{4})}{x^{4 v^{3}}}$

$\frac{3 x^{5} v^{4} - 2 x v^{4}}{x^{4 v^{3}}}$

Step 8

Split the fraction $\frac{3 x^{5} v^{4} - 2 x v^{4}}{x^{4 v^{3}}}$ into two fractions.

$\frac{3 x^{5} v^{4}}{x^{4 v^{3}}} + \frac{- 2 x v^{4}}{x^{4 v^{3}}}$

Step 9

Cancel the common factor of $x^{5}$ and $x^{4 v^{3}}$ .

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Step 9.1

Factor $x^{4 v^{3}}$ out of $3 x^{5} v^{4}$ .

$\frac{x^{4 v^{3}} (3 x^{5 - 4 v^{3}} v^{4})}{x^{4 v^{3}}} + \frac{- 2 x v^{4}}{x^{4 v^{3}}}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Multiply by $1$ .

$\frac{x^{4 v^{3}} (3 x^{5 - 4 v^{3}} v^{4})}{x^{4 v^{3}} \cdot 1} + \frac{- 2 x v^{4}}{x^{4 v^{3}}}$

Step 9.2.2

Cancel the common factor.

$\frac{x^{4 v^{3}} (3 x^{5 - 4 v^{3}} v^{4})}{x^{4 v^{3}} \cdot 1} + \frac{- 2 x v^{4}}{x^{4 v^{3}}}$

Step 9.2.3

Rewrite the expression.

$\frac{3 x^{5 - 4 v^{3}} v^{4}}{1} + \frac{- 2 x v^{4}}{x^{4 v^{3}}}$

Step 9.2.4

Divide $3 x^{5 - 4 v^{3}} v^{4}$ by $1$ .

$3 x^{5 - 4 v^{3}} v^{4} + \frac{- 2 x v^{4}}{x^{4 v^{3}}}$

Step 10

Reorder factors in $3 x^{5 - 4 v^{3}} v^{4}$ .

$3 v^{4} x^{5 - 4 v^{3}} + \frac{- 2 x v^{4}}{x^{4 v^{3}}}$

Step 11

Move the negative in front of the fraction.

$3 v^{4} x^{5 - 4 v^{3}} - \frac{2 x v^{4}}{x^{4 v^{3}}}$