Finite Math Examples

$f (20) = \frac{4}{x + 3} + \frac{24}{x^{2} + 6 x + 9}$

Step 1

Replace the variable $x$ with $20$ in the expression.

$f (20) = \frac{4}{(20) + 3} + \frac{24}{{(20)}^{2} + 6 (20) + 9}$

Step 2

Simplify the result.

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Step 2.1

Simplify each term.

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Step 2.1.1

Add $20$ and $3$ .

$f (20) = \frac{4}{23} + \frac{24}{{(20)}^{2} + 6 (20) + 9}$

Step 2.1.2

Simplify the denominator.

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Step 2.1.2.1

Raise $20$ to the power of $2$ .

$f (20) = \frac{4}{23} + \frac{24}{400 + 6 (20) + 9}$

Step 2.1.2.2

Multiply $6$ by $20$ .

$f (20) = \frac{4}{23} + \frac{24}{400 + 120 + 9}$

Step 2.1.2.3

Add $400$ and $120$ .

$f (20) = \frac{4}{23} + \frac{24}{520 + 9}$

Step 2.1.2.4

Add $520$ and $9$ .

$f (20) = \frac{4}{23} + \frac{24}{529}$

Step 2.2

To write $\frac{4}{23}$ as a fraction with a common denominator, multiply by $\frac{23}{23}$ .

$f (20) = \frac{4}{23} \cdot \frac{23}{23} + \frac{24}{529}$

Step 2.3

Write each expression with a common denominator of $529$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

Multiply $\frac{4}{23}$ by $\frac{23}{23}$ .

$f (20) = \frac{4 \cdot 23}{23 \cdot 23} + \frac{24}{529}$

Step 2.3.2

Multiply $23$ by $23$ .

$f (20) = \frac{4 \cdot 23}{529} + \frac{24}{529}$

Step 2.4

Combine the numerators over the common denominator.

$f (20) = \frac{4 \cdot 23 + 24}{529}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $4$ by $23$ .

$f (20) = \frac{92 + 24}{529}$

Step 2.5.2

Add $92$ and $24$ .

$f (20) = \frac{116}{529}$

Step 2.6

The final answer is $\frac{116}{529}$ .

$\frac{116}{529}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{116}{529}$

Decimal Form:

$0.21928166 \dots$

Step 4