Trigonometry Examples

$\frac{x^{3} + 4 x^{2}}{x^{3} - 7 x^{2} - 44 x}$

Step 1

Factor $x^{2}$ out of $x^{3} + 4 x^{2}$ .

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Step 1.1

Factor $x^{2}$ out of $x^{3}$ .

$\frac{x^{2} x + 4 x^{2}}{x^{3} - 7 x^{2} - 44 x}$

Step 1.2

Factor $x^{2}$ out of $4 x^{2}$ .

$\frac{x^{2} x + x^{2} \cdot 4}{x^{3} - 7 x^{2} - 44 x}$

Step 1.3

Factor $x^{2}$ out of $x^{2} x + x^{2} \cdot 4$ .

$\frac{x^{2} (x + 4)}{x^{3} - 7 x^{2} - 44 x}$

Step 2

Simplify the denominator.

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Step 2.1

Factor $x$ out of $x^{3} - 7 x^{2} - 44 x$ .

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Step 2.1.1

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

$\frac{x^{2} (x + 4)}{x \cdot x^{2} - 7 x^{2} - 44 x}$

Step 2.1.2

Factor $x$ out of $- 7 x^{2}$ .

$\frac{x^{2} (x + 4)}{x \cdot x^{2} + x (- 7 x) - 44 x}$

Step 2.1.3

Factor $x$ out of $- 44 x$ .

$\frac{x^{2} (x + 4)}{x \cdot x^{2} + x (- 7 x) + x \cdot - 44}$

Step 2.1.4

Factor $x$ out of $x \cdot x^{2} + x (- 7 x)$ .

$\frac{x^{2} (x + 4)}{x (x^{2} - 7 x) + x \cdot - 44}$

Step 2.1.5

Factor $x$ out of $x (x^{2} - 7 x) + x \cdot - 44$ .

$\frac{x^{2} (x + 4)}{x (x^{2} - 7 x - 44)}$

Step 2.2

Factor $x^{2} - 7 x - 44$ using the AC method.

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Step 2.2.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 44$ and whose sum is $- 7$ .

$- 11, 4$

Step 2.2.2

Write the factored form using these integers.

$\frac{x^{2} (x + 4)}{x ((x - 11) (x + 4))}$

$\frac{x^{2} (x + 4)}{x (x - 11) (x + 4)}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Cancel the common factor of $x^{2}$ and $x$ .

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Step 3.1.1

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

$\frac{x (x (x + 4))}{x (x - 11) (x + 4)}$

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

Factor $x$ out of $x (x - 11) (x + 4)$ .

$\frac{x (x (x + 4))}{x ((x - 11) (x + 4))}$

Step 3.1.2.2

Cancel the common factor.

$\frac{x (x (x + 4))}{x ((x - 11) (x + 4))}$

Step 3.1.2.3

Rewrite the expression.

$\frac{x (x + 4)}{(x - 11) (x + 4)}$

Step 3.2

Cancel the common factor of $x + 4$ .

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Step 3.2.1

Cancel the common factor.

$\frac{x (x + 4)}{(x - 11) (x + 4)}$

Step 3.2.2

Rewrite the expression.

$\frac{x}{x - 11}$