Basic Math Examples

$\frac{9 y^{4} + 10 y^{2} - 1}{y - \frac{1}{9}}$

Step 1

Multiply the numerator and denominator of the fraction by $9$ .

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Step 1.1

Multiply $\frac{9 y^{4} + 10 y^{2} - 1}{y - \frac{1}{9}}$ by $\frac{9}{9}$ .

$\frac{9}{9} \cdot \frac{9 y^{4} + 10 y^{2} - 1}{y - \frac{1}{9}}$

Step 1.2

Combine.

$\frac{9 (9 y^{4} + 10 y^{2} - 1)}{9 (y - \frac{1}{9})}$

Step 2

Apply the distributive property.

$\frac{9 (9 y^{4}) + 9 (10 y^{2}) + 9 \cdot - 1}{9 y + 9 (- \frac{1}{9})}$

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $9$ .

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Step 3.1.1

Move the leading negative in $- \frac{1}{9}$ into the numerator.

$\frac{9 (9 y^{4}) + 9 (10 y^{2}) + 9 \cdot - 1}{9 y + 9 (\frac{- 1}{9})}$

Step 3.1.2

Cancel the common factor.

$\frac{9 (9 y^{4}) + 9 (10 y^{2}) + 9 \cdot - 1}{9 y + 9 (\frac{- 1}{9})}$

Step 3.1.3

Rewrite the expression.

$\frac{9 (9 y^{4}) + 9 (10 y^{2}) + 9 \cdot - 1}{9 y - 1}$

Step 3.2

Factor $9$ out of $9 \cdot 9 y^{4} + 9 \cdot 10 y^{2} + 9 \cdot - 1$ .

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Step 3.2.1

Factor $9$ out of $9 \cdot 9 y^{4}$ .

$\frac{9 (9 y^{4}) + 9 \cdot 10 y^{2} + 9 \cdot - 1}{9 y - 1}$

Step 3.2.2

Factor $9$ out of $9 \cdot 10 y^{2}$ .

$\frac{9 (9 y^{4}) + 9 (10 y^{2}) + 9 \cdot - 1}{9 y - 1}$

Step 3.2.3

Factor $9$ out of $9 \cdot - 1$ .

$\frac{9 (9 y^{4}) + 9 (10 y^{2}) + 9 (- 1)}{9 y - 1}$

Step 3.2.4

Factor $9$ out of $9 (9 y^{4}) + 9 (10 y^{2})$ .

$\frac{9 (9 y^{4} + 10 y^{2}) + 9 (- 1)}{9 y - 1}$

Step 3.2.5

Factor $9$ out of $9 (9 y^{4} + 10 y^{2}) + 9 (- 1)$ .

$\frac{9 (9 y^{4} + 10 y^{2} - 1)}{9 y - 1}$