Algebra Examples

$f (x) = \frac{6 x + 8}{x - 1}$

Step 1

Write $f (x) = \frac{6 x + 8}{x - 1}$ as an equation.

$y = \frac{6 x + 8}{x - 1}$

Step 2

Factor $2$ out of $6 x + 8$ .

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Step 2.1

Factor $2$ out of $6 x$ .

$y = \frac{2 (3 x) + 8}{x - 1}$

Step 2.2

Factor $2$ out of $8$ .

$y = \frac{2 (3 x) + 2 (4)}{x - 1}$

Step 2.3

Factor $2$ out of $2 (3 x) + 2 (4)$ .

$y = \frac{2 (3 x + 4)}{x - 1}$

Step 3

Choose any value for $x$ that is in the domain to plug into the equation.

Step 4

Choose $0$ to substitute in for $x$ to find the ordered pair.

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Step 4.1

Remove parentheses.

$y = \frac{2 (3 (0) + 4)}{0 - 1}$

Step 4.2

Remove parentheses.

$y = \frac{2 (3 (0) + 4)}{(0) - 1}$

Step 4.3

Simplify $\frac{2 (3 (0) + 4)}{(0) - 1}$ .

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Step 4.3.1

Simplify the numerator.

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Step 4.3.1.1

Multiply $3$ by $0$ .

$y = \frac{2 (0 + 4)}{0 - 1}$

Step 4.3.1.2

Add $0$ and $4$ .

$y = \frac{2 \cdot 4}{0 - 1}$

Step 4.3.2

Simplify the expression.

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Step 4.3.2.1

Subtract $1$ from $0$ .

$y = \frac{2 \cdot 4}{- 1}$

Step 4.3.2.2

Multiply $2$ by $4$ .

$y = \frac{8}{- 1}$

Step 4.3.2.3

Divide $8$ by $- 1$ .

$y = - 8$

Step 4.4

Use the $x$ and $y$ values to form the ordered pair.

$(0, - 8)$

Step 5

Choose $2$ to substitute in for $x$ to find the ordered pair.

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Step 5.1

Remove parentheses.

$y = \frac{2 (3 (2) + 4)}{2 - 1}$

Step 5.2

Remove parentheses.

$y = \frac{2 (3 (2) + 4)}{(2) - 1}$

Step 5.3

Simplify $\frac{2 (3 (2) + 4)}{(2) - 1}$ .

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Step 5.3.1

Simplify the numerator.

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Step 5.3.1.1

Multiply $3$ by $2$ .

$y = \frac{2 (6 + 4)}{2 - 1}$

Step 5.3.1.2

Add $6$ and $4$ .

$y = \frac{2 \cdot 10}{2 - 1}$

Step 5.3.2

Simplify the expression.

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Step 5.3.2.1

Subtract $1$ from $2$ .

$y = \frac{2 \cdot 10}{1}$

Step 5.3.2.2

Multiply $2$ by $10$ .

$y = \frac{20}{1}$

Step 5.3.2.3

Divide $20$ by $1$ .

$y = 20$

Step 5.4

Use the $x$ and $y$ values to form the ordered pair.

$(2, 20)$

Step 6

Choose $3$ to substitute in for $x$ to find the ordered pair.

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Step 6.1

Remove parentheses.

$y = \frac{2 (3 (3) + 4)}{3 - 1}$

Step 6.2

Remove parentheses.

$y = \frac{2 (3 (3) + 4)}{(3) - 1}$

Step 6.3

Simplify $\frac{2 (3 (3) + 4)}{(3) - 1}$ .

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Step 6.3.1

Simplify the numerator.

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Step 6.3.1.1

Multiply $3$ by $3$ .

$y = \frac{2 (9 + 4)}{3 - 1}$

Step 6.3.1.2

Add $9$ and $4$ .

$y = \frac{2 \cdot 13}{3 - 1}$

Step 6.3.2

Simplify the expression.

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Step 6.3.2.1

Subtract $1$ from $3$ .

$y = \frac{2 \cdot 13}{2}$

Step 6.3.2.2

Multiply $2$ by $13$ .

$y = \frac{26}{2}$

Step 6.3.2.3

Divide $26$ by $2$ .

$y = 13$

Step 6.4

Use the $x$ and $y$ values to form the ordered pair.

$(3, 13)$

Step 7

These are three possible solutions to the equation.

$(0, - 8), (2, 20), (3, 13)$

Step 8