Precalculus Examples

$f (20) = \frac{11 x^{2} + 40 x + 1040}{12 x^{2} + 230 x + 2190}$

Step 1

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

$f (20) = \frac{11 {(20)}^{2} + 40 (20) + 1040}{12 {(20)}^{2} + 230 (20) + 2190}$

Step 2

Simplify the result.

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Step 2.1

Simplify the numerator.

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Step 2.1.1

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

$f (20) = \frac{11 \cdot 400 + 40 (20) + 1040}{12 \cdot 20^{2} + 230 (20) + 2190}$

Step 2.1.2

Multiply $11$ by $400$ .

$f (20) = \frac{4400 + 40 (20) + 1040}{12 \cdot 20^{2} + 230 (20) + 2190}$

Step 2.1.3

Multiply $40$ by $20$ .

$f (20) = \frac{4400 + 800 + 1040}{12 \cdot 20^{2} + 230 (20) + 2190}$

Step 2.1.4

Add $4400$ and $800$ .

$f (20) = \frac{5200 + 1040}{12 \cdot 20^{2} + 230 (20) + 2190}$

Step 2.1.5

Add $5200$ and $1040$ .

$f (20) = \frac{6240}{12 \cdot 20^{2} + 230 (20) + 2190}$

Step 2.2

Simplify the denominator.

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Step 2.2.1

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

$f (20) = \frac{6240}{12 \cdot 400 + 230 (20) + 2190}$

Step 2.2.2

Multiply $12$ by $400$ .

$f (20) = \frac{6240}{4800 + 230 (20) + 2190}$

Step 2.2.3

Multiply $230$ by $20$ .

$f (20) = \frac{6240}{4800 + 4600 + 2190}$

Step 2.2.4

Add $4800$ and $4600$ .

$f (20) = \frac{6240}{9400 + 2190}$

Step 2.2.5

Add $9400$ and $2190$ .

$f (20) = \frac{6240}{11590}$

Step 2.3

Cancel the common factor of $6240$ and $11590$ .

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Step 2.3.1

Factor $10$ out of $6240$ .

$f (20) = \frac{10 (624)}{11590}$

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Factor $10$ out of $11590$ .

$f (20) = \frac{10 \cdot 624}{10 \cdot 1159}$

Step 2.3.2.2

Cancel the common factor.

$f (20) = \frac{10 \cdot 624}{10 \cdot 1159}$

Step 2.3.2.3

Rewrite the expression.

$f (20) = \frac{624}{1159}$

Step 2.4

The final answer is $\frac{624}{1159}$ .

$\frac{624}{1159}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{624}{1159}$

Decimal Form:

$0.53839516 \dots$

Step 4