Precalculus Examples

$a n = 8 n - 2$

Step 1

Divide each term in $a n = 8 n - 2$ by $n$ and simplify.

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Step 1.1

Divide each term in $a n = 8 n - 2$ by $n$ .

$\frac{a n}{n} = \frac{8 n}{n} + \frac{- 2}{n}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $n$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{a n}{n} = \frac{8 n}{n} + \frac{- 2}{n}$

Step 1.2.1.2

Divide $a$ by $1$ .

$a = \frac{8 n}{n} + \frac{- 2}{n}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Cancel the common factor of $n$ .

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Step 1.3.1.1.1

Cancel the common factor.

$a = \frac{8 n}{n} + \frac{- 2}{n}$

Step 1.3.1.1.2

Divide $8$ by $1$ .

$a = 8 + \frac{- 2}{n}$

Step 1.3.1.2

Move the negative in front of the fraction.

$a = 8 - \frac{2}{n}$

Step 2

To rewrite as a function of $n$ , write the equation so that $a$ is by itself on one side of the equal sign and an expression involving only $n$ is on the other side.

$f (n) = 8 - \frac{2}{n}$