Finite Math Examples

$\frac{x^{3} - 729}{x - 9}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $729$ as $9^{3}$ .

$\frac{x^{3} - 9^{3}}{x - 9}$

Step 1.2

Since both terms are perfect cubes, factor using the difference of cubes formula, $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$ where $a = x$ and $b = 9$ .

$\frac{(x - 9) (x^{2} + x \cdot 9 + 9^{2})}{x - 9}$

Step 1.3

Simplify.

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Step 1.3.1

Move $9$ to the left of $x$ .

$\frac{(x - 9) (x^{2} + 9 \cdot x + 9^{2})}{x - 9}$

Step 1.3.2

Raise $9$ to the power of $2$ .

$\frac{(x - 9) (x^{2} + 9 x + 81)}{x - 9}$

Step 2

Cancel the common factor of $x - 9$ .

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Step 2.1

Cancel the common factor.

$\frac{(x - 9) (x^{2} + 9 x + 81)}{x - 9}$

Step 2.2

Divide $x^{2} + 9 x + 81$ by $1$ .

$x^{2} + 9 x + 81$