Algebra Examples

$a_{n} = \frac{n^{2} - n}{4 n - 18}$

Step 1

Substitute in the value of $n$ to find the $n$ th term.

$a_{3} = \frac{{(3)}^{2} - (3)}{4 (3) - 18}$

Step 2

Cancel the common factor of ${(3)}^{2} - (3)$ and $4 (3) - 18$ .

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Step 2.1

Factor $3$ out of ${(3)}^{2}$ .

$a_{3} = \frac{3 \cdot 3 - (3)}{4 (3) - 18}$

Step 2.2

Factor $3$ out of $- (3)$ .

$a_{3} = \frac{3 \cdot 3 + 3 \cdot - 1}{4 (3) - 18}$

Step 2.3

Factor $3$ out of $3 \cdot 3 + 3 \cdot - 1$ .

$a_{3} = \frac{3 \cdot (3 - 1)}{4 (3) - 18}$

Step 2.4

Cancel the common factors.

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Step 2.4.1

Factor $3$ out of $4 (3)$ .

$a_{3} = \frac{3 \cdot (3 - 1)}{3 \cdot 4 - 18}$

Step 2.4.2

Factor $3$ out of $- 18$ .

$a_{3} = \frac{3 \cdot (3 - 1)}{3 \cdot 4 + 3 (- 6)}$

Step 2.4.3

Factor $3$ out of $3 \cdot 4 + 3 (- 6)$ .

$a_{3} = \frac{3 \cdot (3 - 1)}{3 \cdot (4 - 6)}$

Step 2.4.4

Cancel the common factor.

$a_{3} = \frac{3 \cdot (3 - 1)}{3 \cdot (4 - 6)}$

Step 2.4.5

Rewrite the expression.

$a_{3} = \frac{3 - 1}{4 - 6}$

Step 3

Simplify the expression.

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Step 3.1

Subtract $1$ from $3$ .

$a_{3} = \frac{2}{4 - 6}$

Step 3.2

Subtract $6$ from $4$ .

$a_{3} = \frac{2}{- 2}$

Step 3.3

Divide $2$ by $- 2$ .

$a_{3} = - 1$