Finite Math Examples

\frac{\sin (2 x)}{x^{2} \sin (x)} - \frac{2}{x^{2}}

$\frac{\sin (2 x)}{x^{2} \sin (x)} - \frac{2}{x^{2}}$

Step 1

Simplify each term.

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Step 1.1

Apply the sine double-angle identity.

\frac{2 \sin (x) \cos (x)}{x^{2} \sin (x)} - \frac{2}{x^{2}}

$\frac{2 \sin (x) \cos (x)}{x^{2} \sin (x)} - \frac{2}{x^{2}}$

Step 1.2

Cancel the common factor of

\sin (x)

$\sin (x)$ .

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Step 1.2.1

Cancel the common factor.

\frac{2 \sin (x) \cos (x)}{x^{2} \sin (x)} - \frac{2}{x^{2}}

$\frac{2 \sin (x) \cos (x)}{x^{2} \sin (x)} - \frac{2}{x^{2}}$

Step 1.2.2

Rewrite the expression.

\frac{2 \cos (x)}{x^{2}} - \frac{2}{x^{2}}

$\frac{2 \cos (x)}{x^{2}} - \frac{2}{x^{2}}$

\frac{2 \cos (x)}{x^{2}} - \frac{2}{x^{2}}

$\frac{2 \cos (x)}{x^{2}} - \frac{2}{x^{2}}$

\frac{2 \cos (x)}{x^{2}} - \frac{2}{x^{2}}

$\frac{2 \cos (x)}{x^{2}} - \frac{2}{x^{2}}$

Step 2

Factor out the GCF of

\frac{1}{x^{2}}

$\frac{1}{x^{2}}$ from

\frac{2 \cos (x)}{x^{2}} - \frac{2}{x^{2}}

$\frac{2 \cos (x)}{x^{2}} - \frac{2}{x^{2}}$ .

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Step 2.1

Factor out the GCF of

\frac{1}{x^{2}}

$\frac{1}{x^{2}}$ from each term in the polynomial.

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Step 2.1.1

Factor out the GCF of

\frac{1}{x^{2}}

$\frac{1}{x^{2}}$ from the expression

\frac{2 \cos (x)}{x^{2}}

$\frac{2 \cos (x)}{x^{2}}$ .

\frac{1 (2 \cos (x))}{x^{2}} - \frac{2}{x^{2}}

$\frac{1 (2 \cos (x))}{x^{2}} - \frac{2}{x^{2}}$

Step 2.1.2

Factor out the GCF of

\frac{1}{x^{2}}

$\frac{1}{x^{2}}$ from the expression

- \frac{2}{x^{2}}

$- \frac{2}{x^{2}}$ .

\frac{1 (2 \cos (x))}{x^{2}} + \frac{1 (- 2)}{x^{2}}

$\frac{1 (2 \cos (x))}{x^{2}} + \frac{1 (- 2)}{x^{2}}$

\frac{1 (2 \cos (x))}{x^{2}} + \frac{1 (- 2)}{x^{2}}

$\frac{1 (2 \cos (x))}{x^{2}} + \frac{1 (- 2)}{x^{2}}$

Step 2.2

Since all the terms share a common factor of

\frac{1}{x^{2}}

$\frac{1}{x^{2}}$ , it can be factored out of each term.

\frac{1 (2 \cos (x) - 2)}{x^{2}}

$\frac{1 (2 \cos (x) - 2)}{x^{2}}$

\frac{1 (2 \cos (x) - 2)}{x^{2}}

$\frac{1 (2 \cos (x) - 2)}{x^{2}}$

Step 3

The polynomial cannot be factored using the specified method. Try a different method, or if you aren't sure, choose Factor.

The polynomial cannot be factored using the specified method.