Finite Math Examples

$f (x) = \frac{2}{x} - x^{2}$ , $x = 6$

Step 1

Replace the variable $x$ with $6$ in the expression.

$f (6) = \frac{2}{6} - {(6)}^{2}$

Step 2

Simplify the result.

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Step 2.1

Simplify each term.

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Step 2.1.1

Cancel the common factor of $2$ and $6$ .

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Step 2.1.1.1

Factor $2$ out of $2$ .

$f (6) = \frac{2 (1)}{6} - {(6)}^{2}$

Step 2.1.1.2

Cancel the common factors.

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Step 2.1.1.2.1

Factor $2$ out of $6$ .

$f (6) = \frac{2 \cdot 1}{2 \cdot 3} - {(6)}^{2}$

Step 2.1.1.2.2

Cancel the common factor.

$f (6) = \frac{2 \cdot 1}{2 \cdot 3} - {(6)}^{2}$

Step 2.1.1.2.3

Rewrite the expression.

$f (6) = \frac{1}{3} - {(6)}^{2}$

Step 2.1.2

Raise $6$ to the power of $2$ .

$f (6) = \frac{1}{3} - 1 \cdot 36$

Step 2.1.3

Multiply $- 1$ by $36$ .

$f (6) = \frac{1}{3} - 36$

Step 2.2

To write $- 36$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$f (6) = \frac{1}{3} - 36 \cdot \frac{3}{3}$

Step 2.3

Combine $- 36$ and $\frac{3}{3}$ .

$f (6) = \frac{1}{3} + \frac{- 36 \cdot 3}{3}$

Step 2.4

Combine the numerators over the common denominator.

$f (6) = \frac{1 - 36 \cdot 3}{3}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $- 36$ by $3$ .

$f (6) = \frac{1 - 108}{3}$

Step 2.5.2

Subtract $108$ from $1$ .

$f (6) = \frac{- 107}{3}$

Step 2.6

Move the negative in front of the fraction.

$f (6) = - \frac{107}{3}$

Step 2.7

The final answer is $- \frac{107}{3}$ .

$- \frac{107}{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- \frac{107}{3}$

Decimal Form:

$- 35.\overline{6}$

Mixed Number Form:

$- 35 \frac{2}{3}$

Step 4