Linear Algebra Examples

a n = 14 + (n - 1) (- 3)

$a n = 14 + (n - 1) (- 3)$

Step 1

Divide each term in

a n = 14 + (n - 1) \cdot - 3

$a n = 14 + (n - 1) \cdot - 3$ by

n

$n$ and simplify.

Tap for more steps...

Step 1.1

Divide each term in

a n = 14 + (n - 1) \cdot - 3

$a n = 14 + (n - 1) \cdot - 3$ by

n

$n$ .

\frac{a n}{n} = \frac{14}{n} + \frac{(n - 1) \cdot - 3}{n}

$\frac{a n}{n} = \frac{14}{n} + \frac{(n - 1) \cdot - 3}{n}$

Step 1.2

Simplify the left side.

Tap for more steps...

Step 1.2.1

Cancel the common factor of

n

$n$ .

Tap for more steps...

Step 1.2.1.1

Cancel the common factor.

\frac{a n}{n} = \frac{14}{n} + \frac{(n - 1) \cdot - 3}{n}

$\frac{a n}{n} = \frac{14}{n} + \frac{(n - 1) \cdot - 3}{n}$

Step 1.2.1.2

Divide

a

$a$ by

1

$1$ .

a = \frac{14}{n} + \frac{(n - 1) \cdot - 3}{n}

$a = \frac{14}{n} + \frac{(n - 1) \cdot - 3}{n}$

a = \frac{14}{n} + \frac{(n - 1) \cdot - 3}{n}

$a = \frac{14}{n} + \frac{(n - 1) \cdot - 3}{n}$

a = \frac{14}{n} + \frac{(n - 1) \cdot - 3}{n}

$a = \frac{14}{n} + \frac{(n - 1) \cdot - 3}{n}$

Step 1.3

Simplify the right side.

Tap for more steps...

Step 1.3.1

Combine the numerators over the common denominator.

a = \frac{14 + (n - 1) \cdot - 3}{n}

$a = \frac{14 + (n - 1) \cdot - 3}{n}$

Step 1.3.2

Simplify each term.

Tap for more steps...

Step 1.3.2.1

Apply the distributive property.

a = \frac{14 + n \cdot - 3 - 1 \cdot - 3}{n}

$a = \frac{14 + n \cdot - 3 - 1 \cdot - 3}{n}$

Step 1.3.2.2

Move

- 3

$- 3$ to the left of

n

$n$ .

a = \frac{14 - 3 \cdot n - 1 \cdot - 3}{n}

$a = \frac{14 - 3 \cdot n - 1 \cdot - 3}{n}$

Step 1.3.2.3

Multiply

- 1

$- 1$ by

- 3

$- 3$ .

a = \frac{14 - 3 n + 3}{n}

$a = \frac{14 - 3 n + 3}{n}$

a = \frac{14 - 3 n + 3}{n}

$a = \frac{14 - 3 n + 3}{n}$

Step 1.3.3

Simplify with factoring out.

Tap for more steps...

Step 1.3.3.1

Add

14

$14$ and

3

$3$ .

a = \frac{- 3 n + 17}{n}

$a = \frac{- 3 n + 17}{n}$

Step 1.3.3.2

Factor

- 1

$- 1$ out of

- 3 n

$- 3 n$ .

a = \frac{- (3 n) + 17}{n}

$a = \frac{- (3 n) + 17}{n}$

Step 1.3.3.3

Rewrite

17

$17$ as

- 1 (- 17)

$- 1 (- 17)$ .

a = \frac{- (3 n) - 1 (- 17)}{n}

$a = \frac{- (3 n) - 1 (- 17)}{n}$

Step 1.3.3.4

Factor

- 1

$- 1$ out of

- (3 n) - 1 (- 17)

$- (3 n) - 1 (- 17)$ .

a = \frac{- (3 n - 17)}{n}

$a = \frac{- (3 n - 17)}{n}$

Step 1.3.3.5

Simplify the expression.

Tap for more steps...

Step 1.3.3.5.1

Rewrite

- (3 n - 17)

$- (3 n - 17)$ as

- 1 (3 n - 17)

$- 1 (3 n - 17)$ .

a = \frac{- 1 (3 n - 17)}{n}

$a = \frac{- 1 (3 n - 17)}{n}$

Step 1.3.3.5.2

Move the negative in front of the fraction.

a = - \frac{3 n - 17}{n}

$a = - \frac{3 n - 17}{n}$

a = - \frac{3 n - 17}{n}

$a = - \frac{3 n - 17}{n}$

a = - \frac{3 n - 17}{n}

$a = - \frac{3 n - 17}{n}$

a = - \frac{3 n - 17}{n}

$a = - \frac{3 n - 17}{n}$

a = - \frac{3 n - 17}{n}

$a = - \frac{3 n - 17}{n}$

Step 2

Set the denominator in

\frac{3 n - 17}{n}

$\frac{3 n - 17}{n}$ equal to

0

$0$ to find where the expression is undefined.

n = 0

$n = 0$

Step 3

The domain is all values of

n

$n$ that make the expression defined.

Interval Notation:

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

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

Set-Builder Notation:

{n | n \neq 0}

${n | n \neq 0}$

Step 4

[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$