Linear Algebra Examples

$(s n) = (n - 2)$

Step 1

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

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Step 1.1

Divide each term in $s n = n - 2$ by $n$ .

$\frac{s n}{n} = \frac{n}{n} + \frac{- 2}{n}$

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.

$\frac{s n}{n} = \frac{n}{n} + \frac{- 2}{n}$

Step 1.2.1.2

Divide $s$ by $1$ .

$s = \frac{n}{n} + \frac{- 2}{n}$

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.

$s = \frac{n}{n} + \frac{- 2}{n}$

Step 1.3.1.1.2

Rewrite the expression.

$s = 1 + \frac{- 2}{n}$

Step 1.3.1.2

Move the negative in front of the fraction.

$s = 1 - \frac{2}{n}$

Step 2

Set the denominator in $\frac{2}{n}$ equal to $0$ to find where the expression is undefined.

$n = 0$

Step 3

The domain is all values of $n$ that make the expression defined.

Interval Notation:

$(- \infty, 0) \cup (0, \infty)$

Set-Builder Notation:

${n | n \neq 0}$

Step 4