Pre-Algebra Examples

$\frac{9 y^{4} - 15 y - 6 y^{2}}{3 y^{2}}$

Step 1

Simplify the numerator.

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Step 1.1

Factor $3 y$ out of $9 y^{4} - 15 y - 6 y^{2}$ .

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Step 1.1.1

Factor $3 y$ out of $9 y^{4}$ .

$\frac{3 y (3 y^{3}) - 15 y - 6 y^{2}}{3 y^{2}}$

Step 1.1.2

Factor $3 y$ out of $- 15 y$ .

$\frac{3 y (3 y^{3}) + 3 y (- 5) - 6 y^{2}}{3 y^{2}}$

Step 1.1.3

Factor $3 y$ out of $- 6 y^{2}$ .

$\frac{3 y (3 y^{3}) + 3 y (- 5) + 3 y (- 2 y)}{3 y^{2}}$

Step 1.1.4

Factor $3 y$ out of $3 y (3 y^{3}) + 3 y (- 5)$ .

$\frac{3 y (3 y^{3} - 5) + 3 y (- 2 y)}{3 y^{2}}$

Step 1.1.5

Factor $3 y$ out of $3 y (3 y^{3} - 5) + 3 y (- 2 y)$ .

$\frac{3 y (3 y^{3} - 5 - 2 y)}{3 y^{2}}$

Step 1.2

Reorder terms.

$\frac{3 y (3 y^{3} - 2 y - 5)}{3 y^{2}}$

Step 2

Cancel the common factor of $3$ .

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Step 2.1

Cancel the common factor.

$\frac{3 y (3 y^{3} - 2 y - 5)}{3 y^{2}}$

Step 2.2

Rewrite the expression.

$\frac{y (3 y^{3} - 2 y - 5)}{y^{2}}$

Step 3

Cancel the common factors.

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Step 3.1

Factor $y$ out of $y^{2}$ .

$\frac{y (3 y^{3} - 2 y - 5)}{y \cdot y}$

Step 3.2

Cancel the common factor.

$\frac{y (3 y^{3} - 2 y - 5)}{y \cdot y}$

Step 3.3

Rewrite the expression.

$\frac{3 y^{3} - 2 y - 5}{y}$

Step 4

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

$\frac{3 y^{3} - 2 y}{y} + \frac{- 5}{y}$

Step 5

Split the fraction $\frac{3 y^{3} - 2 y}{y}$ into two fractions.

$\frac{3 y^{3}}{y} + \frac{- 2 y}{y} + \frac{- 5}{y}$

Step 6

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

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Step 6.1

Factor $y$ out of $3 y^{3}$ .

$\frac{y (3 y^{2})}{y} + \frac{- 2 y}{y} + \frac{- 5}{y}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

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

$\frac{y (3 y^{2})}{y^{1}} + \frac{- 2 y}{y} + \frac{- 5}{y}$

Step 6.2.2

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

$\frac{y (3 y^{2})}{y \cdot 1} + \frac{- 2 y}{y} + \frac{- 5}{y}$

Step 6.2.3

Cancel the common factor.

$\frac{y (3 y^{2})}{y \cdot 1} + \frac{- 2 y}{y} + \frac{- 5}{y}$

Step 6.2.4

Rewrite the expression.

$\frac{3 y^{2}}{1} + \frac{- 2 y}{y} + \frac{- 5}{y}$

Step 6.2.5

Divide $3 y^{2}$ by $1$ .

$3 y^{2} + \frac{- 2 y}{y} + \frac{- 5}{y}$

Step 7

Cancel the common factor of $y$ .

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Step 7.1

Cancel the common factor.

$3 y^{2} + \frac{- 2 y}{y} + \frac{- 5}{y}$

Step 7.2

Divide $- 2$ by $1$ .

$3 y^{2} - 2 + \frac{- 5}{y}$

Step 8

Move the negative in front of the fraction.

$3 y^{2} - 2 - \frac{5}{y}$