Calculus Examples

$f (x) = - 2 x^{3} + 21 x^{2} - 60 x$ , $[1, 6]$

Step 1

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 2

$f (x)$ is continuous on $[1, 6]$ .

$f (x)$ is continuous

Step 3

The average value of function $f$ over the interval $[a, b]$ is defined as $A (x) = \frac{1}{b - a} \int_{a}^{b} f (x) d x$ .

$A (x) = \frac{1}{b - a} \int_{a}^{b} f (x) d x$

Step 4

Substitute the actual values into the formula for the average value of a function.

$A (x) = \frac{1}{6 - 1} (\int_{1}^{6} - 2 x^{3} + 21 x^{2} - 60 x d x)$

Step 5

Split the single integral into multiple integrals.

$A (x) = \frac{1}{6 - 1} (\int_{1}^{6} - 2 x^{3} d x + \int_{1}^{6} 21 x^{2} d x + \int_{1}^{6} - 60 x d x)$

Step 6

Since $- 2$ is constant with respect to $x$ , move $- 2$ out of the integral.

$A (x) = \frac{1}{6 - 1} (- 2 \int_{1}^{6} x^{3} d x + \int_{1}^{6} 21 x^{2} d x + \int_{1}^{6} - 60 x d x)$

Step 7

By the Power Rule, the integral of $x^{3}$ with respect to $x$ is $\frac{1}{4} x^{4}$ .

$A (x) = \frac{1}{6 - 1} (- 2 (\frac{1}{4} x^{4}]_{1}^{6}) + \int_{1}^{6} 21 x^{2} d x + \int_{1}^{6} - 60 x d x)$

Step 8

Combine $\frac{1}{4}$ and $x^{4}$ .

$A (x) = \frac{1}{6 - 1} (- 2 (\frac{x^{4}}{4}]_{1}^{6}) + \int_{1}^{6} 21 x^{2} d x + \int_{1}^{6} - 60 x d x)$

Step 9

Since $21$ is constant with respect to $x$ , move $21$ out of the integral.

$A (x) = \frac{1}{6 - 1} (- 2 (\frac{x^{4}}{4}]_{1}^{6}) + 21 \int_{1}^{6} x^{2} d x + \int_{1}^{6} - 60 x d x)$

Step 10

By the Power Rule, the integral of $x^{2}$ with respect to $x$ is $\frac{1}{3} x^{3}$ .

$A (x) = \frac{1}{6 - 1} (- 2 (\frac{x^{4}}{4}]_{1}^{6}) + 21 (\frac{1}{3} x^{3}]_{1}^{6}) + \int_{1}^{6} - 60 x d x)$

Step 11

Combine $\frac{1}{3}$ and $x^{3}$ .

$A (x) = \frac{1}{6 - 1} (- 2 (\frac{x^{4}}{4}]_{1}^{6}) + 21 (\frac{x^{3}}{3}]_{1}^{6}) + \int_{1}^{6} - 60 x d x)$

Step 12

Since $- 60$ is constant with respect to $x$ , move $- 60$ out of the integral.

$A (x) = \frac{1}{6 - 1} (- 2 (\frac{x^{4}}{4}]_{1}^{6}) + 21 (\frac{x^{3}}{3}]_{1}^{6}) - 60 \int_{1}^{6} x d x)$

Step 13

By the Power Rule, the integral of $x$ with respect to $x$ is $\frac{1}{2} x^{2}$ .

$A (x) = \frac{1}{6 - 1} (- 2 (\frac{x^{4}}{4}]_{1}^{6}) + 21 (\frac{x^{3}}{3}]_{1}^{6}) - 60 (\frac{1}{2} x^{2}]_{1}^{6}))$

Step 14

Simplify the answer.

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Step 14.1

Combine $\frac{1}{2}$ and $x^{2}$ .

$A (x) = \frac{1}{6 - 1} (- 2 (\frac{x^{4}}{4}]_{1}^{6}) + 21 (\frac{x^{3}}{3}]_{1}^{6}) - 60 (\frac{x^{2}}{2}]_{1}^{6}))$

Step 14.2

Substitute and simplify.

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Step 14.2.1

Evaluate $\frac{x^{4}}{4}$ at $6$ and at $1$ .

$A (x) = \frac{1}{6 - 1} (- 2 ((\frac{6^{4}}{4}) - \frac{1^{4}}{4}) + 21 (\frac{x^{3}}{3}]_{1}^{6}) - 60 (\frac{x^{2}}{2}]_{1}^{6}))$

Step 14.2.2

Evaluate $\frac{x^{3}}{3}$ at $6$ and at $1$ .

$A (x) = \frac{1}{6 - 1} (- 2 (\frac{6^{4}}{4} - \frac{1^{4}}{4}) + 21 (\frac{6^{3}}{3} - \frac{1^{3}}{3}) - 60 (\frac{x^{2}}{2}]_{1}^{6}))$

Step 14.2.3

Evaluate $\frac{x^{2}}{2}$ at $6$ and at $1$ .

$A (x) = \frac{1}{6 - 1} (- 2 (\frac{6^{4}}{4} - \frac{1^{4}}{4}) + 21 (\frac{6^{3}}{3} - \frac{1^{3}}{3}) - 60 ((\frac{6^{2}}{2}) - \frac{1^{2}}{2}))$

Step 14.2.4

Simplify.

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Step 14.2.4.1

Raise $6$ to the power of $4$ .

$A (x) = \frac{1}{6 - 1} (- 2 (\frac{1296}{4} - \frac{1^{4}}{4}) + 21 (\frac{6^{3}}{3} - \frac{1^{3}}{3}) - 60 ((\frac{6^{2}}{2}) - \frac{1^{2}}{2}))$

Step 14.2.4.2

Cancel the common factor of $1296$ and $4$ .

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Step 14.2.4.2.1

Factor $4$ out of $1296$ .

$A (x) = \frac{1}{6 - 1} (- 2 (\frac{4 \cdot 324}{4} - \frac{1^{4}}{4}) + 21 (\frac{6^{3}}{3} - \frac{1^{3}}{3}) - 60 ((\frac{6^{2}}{2}) - \frac{1^{2}}{2}))$

Step 14.2.4.2.2

Cancel the common factors.

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Step 14.2.4.2.2.1

Factor $4$ out of $4$ .

$A (x) = \frac{1}{6 - 1} (- 2 (\frac{4 \cdot 324}{4 (1)} - \frac{1^{4}}{4}) + 21 (\frac{6^{3}}{3} - \frac{1^{3}}{3}) - 60 ((\frac{6^{2}}{2}) - \frac{1^{2}}{2}))$

Step 14.2.4.2.2.2

Cancel the common factor.

$A (x) = \frac{1}{6 - 1} (- 2 (\frac{4 \cdot 324}{4 \cdot 1} - \frac{1^{4}}{4}) + 21 (\frac{6^{3}}{3} - \frac{1^{3}}{3}) - 60 ((\frac{6^{2}}{2}) - \frac{1^{2}}{2}))$

Step 14.2.4.2.2.3

Rewrite the expression.

$A (x) = \frac{1}{6 - 1} (- 2 (\frac{324}{1} - \frac{1^{4}}{4}) + 21 (\frac{6^{3}}{3} - \frac{1^{3}}{3}) - 60 ((\frac{6^{2}}{2}) - \frac{1^{2}}{2}))$

Step 14.2.4.2.2.4

Divide $324$ by $1$ .

$A (x) = \frac{1}{6 - 1} (- 2 (324 - \frac{1^{4}}{4}) + 21 (\frac{6^{3}}{3} - \frac{1^{3}}{3}) - 60 ((\frac{6^{2}}{2}) - \frac{1^{2}}{2}))$

Step 14.2.4.3

One to any power is one.

$A (x) = \frac{1}{6 - 1} (- 2 (324 - \frac{1}{4}) + 21 (\frac{6^{3}}{3} - \frac{1^{3}}{3}) - 60 ((\frac{6^{2}}{2}) - \frac{1^{2}}{2}))$

Step 14.2.4.4

To write $324$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$A (x) = \frac{1}{6 - 1} (- 2 (324 \cdot \frac{4}{4} - \frac{1}{4}) + 21 (\frac{6^{3}}{3} - \frac{1^{3}}{3}) - 60 ((\frac{6^{2}}{2}) - \frac{1^{2}}{2}))$

Step 14.2.4.5

Combine $324$ and $\frac{4}{4}$ .

$A (x) = \frac{1}{6 - 1} (- 2 (\frac{324 \cdot 4}{4} - \frac{1}{4}) + 21 (\frac{6^{3}}{3} - \frac{1^{3}}{3}) - 60 ((\frac{6^{2}}{2}) - \frac{1^{2}}{2}))$

Step 14.2.4.6

Combine the numerators over the common denominator.

$A (x) = \frac{1}{6 - 1} (- 2 \frac{324 \cdot 4 - 1}{4} + 21 (\frac{6^{3}}{3} - \frac{1^{3}}{3}) - 60 ((\frac{6^{2}}{2}) - \frac{1^{2}}{2}))$

Step 14.2.4.7

Simplify the numerator.

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Step 14.2.4.7.1

Multiply $324$ by $4$ .

$A (x) = \frac{1}{6 - 1} (- 2 \frac{1296 - 1}{4} + 21 (\frac{6^{3}}{3} - \frac{1^{3}}{3}) - 60 ((\frac{6^{2}}{2}) - \frac{1^{2}}{2}))$

Step 14.2.4.7.2

Subtract $1$ from $1296$ .

$A (x) = \frac{1}{6 - 1} (- 2 (\frac{1295}{4}) + 21 (\frac{6^{3}}{3} - \frac{1^{3}}{3}) - 60 ((\frac{6^{2}}{2}) - \frac{1^{2}}{2}))$

Step 14.2.4.8

Combine $- 2$ and $\frac{1295}{4}$ .

$A (x) = \frac{1}{6 - 1} (\frac{- 2 \cdot 1295}{4} + 21 (\frac{6^{3}}{3} - \frac{1^{3}}{3}) - 60 ((\frac{6^{2}}{2}) - \frac{1^{2}}{2}))$

Step 14.2.4.9

Multiply $- 2$ by $1295$ .

$A (x) = \frac{1}{6 - 1} (\frac{- 2590}{4} + 21 (\frac{6^{3}}{3} - \frac{1^{3}}{3}) - 60 ((\frac{6^{2}}{2}) - \frac{1^{2}}{2}))$

Step 14.2.4.10

Cancel the common factor of $- 2590$ and $4$ .

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Step 14.2.4.10.1

Factor $2$ out of $- 2590$ .

$A (x) = \frac{1}{6 - 1} (\frac{2 (- 1295)}{4} + 21 (\frac{6^{3}}{3} - \frac{1^{3}}{3}) - 60 ((\frac{6^{2}}{2}) - \frac{1^{2}}{2}))$

Step 14.2.4.10.2

Cancel the common factors.

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Step 14.2.4.10.2.1

Factor $2$ out of $4$ .

$A (x) = \frac{1}{6 - 1} (\frac{2 \cdot - 1295}{2 \cdot 2} + 21 (\frac{6^{3}}{3} - \frac{1^{3}}{3}) - 60 ((\frac{6^{2}}{2}) - \frac{1^{2}}{2}))$

Step 14.2.4.10.2.2

Cancel the common factor.

$A (x) = \frac{1}{6 - 1} (\frac{2 \cdot - 1295}{2 \cdot 2} + 21 (\frac{6^{3}}{3} - \frac{1^{3}}{3}) - 60 ((\frac{6^{2}}{2}) - \frac{1^{2}}{2}))$

Step 14.2.4.10.2.3

Rewrite the expression.

$A (x) = \frac{1}{6 - 1} (\frac{- 1295}{2} + 21 (\frac{6^{3}}{3} - \frac{1^{3}}{3}) - 60 ((\frac{6^{2}}{2}) - \frac{1^{2}}{2}))$

Step 14.2.4.11

Move the negative in front of the fraction.

$A (x) = \frac{1}{6 - 1} (- \frac{1295}{2} + 21 (\frac{6^{3}}{3} - \frac{1^{3}}{3}) - 60 ((\frac{6^{2}}{2}) - \frac{1^{2}}{2}))$

Step 14.2.4.12

Raise $6$ to the power of $3$ .

$A (x) = \frac{1}{6 - 1} (- \frac{1295}{2} + 21 (\frac{216}{3} - \frac{1^{3}}{3}) - 60 ((\frac{6^{2}}{2}) - \frac{1^{2}}{2}))$

Step 14.2.4.13

Cancel the common factor of $216$ and $3$ .

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Step 14.2.4.13.1

Factor $3$ out of $216$ .

$A (x) = \frac{1}{6 - 1} (- \frac{1295}{2} + 21 (\frac{3 \cdot 72}{3} - \frac{1^{3}}{3}) - 60 ((\frac{6^{2}}{2}) - \frac{1^{2}}{2}))$

Step 14.2.4.13.2

Cancel the common factors.

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Step 14.2.4.13.2.1

Factor $3$ out of $3$ .

$A (x) = \frac{1}{6 - 1} (- \frac{1295}{2} + 21 (\frac{3 \cdot 72}{3 (1)} - \frac{1^{3}}{3}) - 60 ((\frac{6^{2}}{2}) - \frac{1^{2}}{2}))$

Step 14.2.4.13.2.2

Cancel the common factor.

$A (x) = \frac{1}{6 - 1} (- \frac{1295}{2} + 21 (\frac{3 \cdot 72}{3 \cdot 1} - \frac{1^{3}}{3}) - 60 ((\frac{6^{2}}{2}) - \frac{1^{2}}{2}))$

Step 14.2.4.13.2.3

Rewrite the expression.

$A (x) = \frac{1}{6 - 1} (- \frac{1295}{2} + 21 (\frac{72}{1} - \frac{1^{3}}{3}) - 60 ((\frac{6^{2}}{2}) - \frac{1^{2}}{2}))$

Step 14.2.4.13.2.4

Divide $72$ by $1$ .

$A (x) = \frac{1}{6 - 1} (- \frac{1295}{2} + 21 (72 - \frac{1^{3}}{3}) - 60 ((\frac{6^{2}}{2}) - \frac{1^{2}}{2}))$

Step 14.2.4.14

One to any power is one.

$A (x) = \frac{1}{6 - 1} (- \frac{1295}{2} + 21 (72 - \frac{1}{3}) - 60 ((\frac{6^{2}}{2}) - \frac{1^{2}}{2}))$

Step 14.2.4.15

To write $72$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$A (x) = \frac{1}{6 - 1} (- \frac{1295}{2} + 21 (72 \cdot \frac{3}{3} - \frac{1}{3}) - 60 ((\frac{6^{2}}{2}) - \frac{1^{2}}{2}))$

Step 14.2.4.16

Combine $72$ and $\frac{3}{3}$ .

$A (x) = \frac{1}{6 - 1} (- \frac{1295}{2} + 21 (\frac{72 \cdot 3}{3} - \frac{1}{3}) - 60 ((\frac{6^{2}}{2}) - \frac{1^{2}}{2}))$

Step 14.2.4.17

Combine the numerators over the common denominator.

$A (x) = \frac{1}{6 - 1} (- \frac{1295}{2} + 21 (\frac{72 \cdot 3 - 1}{3}) - 60 ((\frac{6^{2}}{2}) - \frac{1^{2}}{2}))$

Step 14.2.4.18

Simplify the numerator.

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Step 14.2.4.18.1

Multiply $72$ by $3$ .

$A (x) = \frac{1}{6 - 1} (- \frac{1295}{2} + 21 (\frac{216 - 1}{3}) - 60 ((\frac{6^{2}}{2}) - \frac{1^{2}}{2}))$

Step 14.2.4.18.2

Subtract $1$ from $216$ .

$A (x) = \frac{1}{6 - 1} (- \frac{1295}{2} + 21 (\frac{215}{3}) - 60 ((\frac{6^{2}}{2}) - \frac{1^{2}}{2}))$

Step 14.2.4.19

Combine $21$ and $\frac{215}{3}$ .

$A (x) = \frac{1}{6 - 1} (- \frac{1295}{2} + \frac{21 \cdot 215}{3} - 60 ((\frac{6^{2}}{2}) - \frac{1^{2}}{2}))$

Step 14.2.4.20

Multiply $21$ by $215$ .

$A (x) = \frac{1}{6 - 1} (- \frac{1295}{2} + \frac{4515}{3} - 60 ((\frac{6^{2}}{2}) - \frac{1^{2}}{2}))$

Step 14.2.4.21

Cancel the common factor of $4515$ and $3$ .

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Step 14.2.4.21.1

Factor $3$ out of $4515$ .

$A (x) = \frac{1}{6 - 1} (- \frac{1295}{2} + \frac{3 \cdot 1505}{3} - 60 ((\frac{6^{2}}{2}) - \frac{1^{2}}{2}))$

Step 14.2.4.21.2

Cancel the common factors.

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Step 14.2.4.21.2.1

Factor $3$ out of $3$ .

$A (x) = \frac{1}{6 - 1} (- \frac{1295}{2} + \frac{3 \cdot 1505}{3 (1)} - 60 ((\frac{6^{2}}{2}) - \frac{1^{2}}{2}))$

Step 14.2.4.21.2.2

Cancel the common factor.

$A (x) = \frac{1}{6 - 1} (- \frac{1295}{2} + \frac{3 \cdot 1505}{3 \cdot 1} - 60 ((\frac{6^{2}}{2}) - \frac{1^{2}}{2}))$

Step 14.2.4.21.2.3

Rewrite the expression.

$A (x) = \frac{1}{6 - 1} (- \frac{1295}{2} + \frac{1505}{1} - 60 ((\frac{6^{2}}{2}) - \frac{1^{2}}{2}))$

Step 14.2.4.21.2.4

Divide $1505$ by $1$ .

$A (x) = \frac{1}{6 - 1} (- \frac{1295}{2} + 1505 - 60 ((\frac{6^{2}}{2}) - \frac{1^{2}}{2}))$

Step 14.2.4.22

To write $1505$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$A (x) = \frac{1}{6 - 1} (- \frac{1295}{2} + 1505 \cdot \frac{2}{2} - 60 ((\frac{6^{2}}{2}) - \frac{1^{2}}{2}))$

Step 14.2.4.23

Combine $1505$ and $\frac{2}{2}$ .

$A (x) = \frac{1}{6 - 1} (- \frac{1295}{2} + \frac{1505 \cdot 2}{2} - 60 ((\frac{6^{2}}{2}) - \frac{1^{2}}{2}))$

Step 14.2.4.24

Combine the numerators over the common denominator.

$A (x) = \frac{1}{6 - 1} (\frac{- 1295 + 1505 \cdot 2}{2} - 60 ((\frac{6^{2}}{2}) - \frac{1^{2}}{2}))$

Step 14.2.4.25

Simplify the numerator.

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Step 14.2.4.25.1

Multiply $1505$ by $2$ .

$A (x) = \frac{1}{6 - 1} (\frac{- 1295 + 3010}{2} - 60 ((\frac{6^{2}}{2}) - \frac{1^{2}}{2}))$

Step 14.2.4.25.2

Add $- 1295$ and $3010$ .

$A (x) = \frac{1}{6 - 1} (\frac{1715}{2} - 60 ((\frac{6^{2}}{2}) - \frac{1^{2}}{2}))$

Step 14.2.4.26

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

$A (x) = \frac{1}{6 - 1} (\frac{1715}{2} - 60 (\frac{36}{2} - \frac{1^{2}}{2}))$

Step 14.2.4.27

Cancel the common factor of $36$ and $2$ .

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Step 14.2.4.27.1

Factor $2$ out of $36$ .

$A (x) = \frac{1}{6 - 1} (\frac{1715}{2} - 60 (\frac{2 \cdot 18}{2} - \frac{1^{2}}{2}))$

Step 14.2.4.27.2

Cancel the common factors.

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Step 14.2.4.27.2.1

Factor $2$ out of $2$ .

$A (x) = \frac{1}{6 - 1} (\frac{1715}{2} - 60 (\frac{2 \cdot 18}{2 (1)} - \frac{1^{2}}{2}))$

Step 14.2.4.27.2.2

Cancel the common factor.

$A (x) = \frac{1}{6 - 1} (\frac{1715}{2} - 60 (\frac{2 \cdot 18}{2 \cdot 1} - \frac{1^{2}}{2}))$

Step 14.2.4.27.2.3

Rewrite the expression.

$A (x) = \frac{1}{6 - 1} (\frac{1715}{2} - 60 (\frac{18}{1} - \frac{1^{2}}{2}))$

Step 14.2.4.27.2.4

Divide $18$ by $1$ .

$A (x) = \frac{1}{6 - 1} (\frac{1715}{2} - 60 (18 - \frac{1^{2}}{2}))$

Step 14.2.4.28

One to any power is one.

$A (x) = \frac{1}{6 - 1} (\frac{1715}{2} - 60 (18 - \frac{1}{2}))$

Step 14.2.4.29

To write $18$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$A (x) = \frac{1}{6 - 1} (\frac{1715}{2} - 60 (18 \cdot \frac{2}{2} - \frac{1}{2}))$

Step 14.2.4.30

Combine $18$ and $\frac{2}{2}$ .

$A (x) = \frac{1}{6 - 1} (\frac{1715}{2} - 60 (\frac{18 \cdot 2}{2} - \frac{1}{2}))$

Step 14.2.4.31

Combine the numerators over the common denominator.

$A (x) = \frac{1}{6 - 1} (\frac{1715}{2} - 60 \frac{18 \cdot 2 - 1}{2})$

Step 14.2.4.32

Simplify the numerator.

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Step 14.2.4.32.1

Multiply $18$ by $2$ .

$A (x) = \frac{1}{6 - 1} (\frac{1715}{2} - 60 \frac{36 - 1}{2})$

Step 14.2.4.32.2

Subtract $1$ from $36$ .

$A (x) = \frac{1}{6 - 1} (\frac{1715}{2} - 60 (\frac{35}{2}))$

Step 14.2.4.33

Combine $- 60$ and $\frac{35}{2}$ .

$A (x) = \frac{1}{6 - 1} (\frac{1715}{2} + \frac{- 60 \cdot 35}{2})$

Step 14.2.4.34

Multiply $- 60$ by $35$ .

$A (x) = \frac{1}{6 - 1} (\frac{1715}{2} + \frac{- 2100}{2})$

Step 14.2.4.35

Cancel the common factor of $- 2100$ and $2$ .

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Step 14.2.4.35.1

Factor $2$ out of $- 2100$ .

$A (x) = \frac{1}{6 - 1} (\frac{1715}{2} + \frac{2 \cdot - 1050}{2})$

Step 14.2.4.35.2

Cancel the common factors.

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Step 14.2.4.35.2.1

Factor $2$ out of $2$ .

$A (x) = \frac{1}{6 - 1} (\frac{1715}{2} + \frac{2 \cdot - 1050}{2 (1)})$

Step 14.2.4.35.2.2

Cancel the common factor.

$A (x) = \frac{1}{6 - 1} (\frac{1715}{2} + \frac{2 \cdot - 1050}{2 \cdot 1})$

Step 14.2.4.35.2.3

Rewrite the expression.

$A (x) = \frac{1}{6 - 1} (\frac{1715}{2} + \frac{- 1050}{1})$

Step 14.2.4.35.2.4

Divide $- 1050$ by $1$ .

$A (x) = \frac{1}{6 - 1} (\frac{1715}{2} - 1050)$

Step 14.2.4.36

To write $- 1050$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$A (x) = \frac{1}{6 - 1} (\frac{1715}{2} - 1050 \cdot \frac{2}{2})$

Step 14.2.4.37

Combine $- 1050$ and $\frac{2}{2}$ .

$A (x) = \frac{1}{6 - 1} (\frac{1715}{2} + \frac{- 1050 \cdot 2}{2})$

Step 14.2.4.38

Combine the numerators over the common denominator.

$A (x) = \frac{1}{6 - 1} (\frac{1715 - 1050 \cdot 2}{2})$

Step 14.2.4.39

Simplify the numerator.

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Step 14.2.4.39.1

Multiply $- 1050$ by $2$ .

$A (x) = \frac{1}{6 - 1} (\frac{1715 - 2100}{2})$

Step 14.2.4.39.2

Subtract $2100$ from $1715$ .

$A (x) = \frac{1}{6 - 1} (\frac{- 385}{2})$

Step 14.2.4.40

Move the negative in front of the fraction.

$A (x) = \frac{1}{6 - 1} (- \frac{385}{2})$

Step 15

Subtract $1$ from $6$ .

$A (x) = \frac{1}{5} \cdot (- \frac{385}{2})$

Step 16

Cancel the common factor of $5$ .

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Step 16.1

Move the leading negative in $- \frac{385}{2}$ into the numerator.

$A (x) = \frac{1}{5} \cdot \frac{- 385}{2}$

Step 16.2

Factor $5$ out of $- 385$ .

$A (x) = \frac{1}{5} \cdot \frac{5 (- 77)}{2}$

Step 16.3

Cancel the common factor.

$A (x) = \frac{1}{5} \cdot \frac{5 \cdot - 77}{2}$

Step 16.4

Rewrite the expression.

$A (x) = \frac{- 77}{2}$

Step 17

Move the negative in front of the fraction.

$A (x) = - \frac{77}{2}$

Step 18