Algebra Examples

$f (x) = \frac{5 x}{x - 2}$

Step 1

Write $f (x) = \frac{5 x}{x - 2}$ as an equation.

$y = \frac{5 x}{x - 2}$

Step 2

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

Step 3

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

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Step 3.1

Remove parentheses.

$y = \frac{5 (0)}{0 - 2}$

Step 3.2

Remove parentheses.

$y = \frac{5 (0)}{(0) - 2}$

Step 3.3

Simplify $\frac{5 (0)}{(0) - 2}$ .

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Step 3.3.1

Cancel the common factor of $0$ and $(0) - 2$ .

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Step 3.3.1.1

Factor $2$ out of $5 (0)$ .

$y = \frac{2 (5 \cdot (0))}{(0) - 2}$

Step 3.3.1.2

Cancel the common factors.

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Step 3.3.1.2.1

Factor $2$ out of $0$ .

$y = \frac{2 (5 \cdot (0))}{2 (0) - 2}$

Step 3.3.1.2.2

Factor $2$ out of $- 2$ .

$y = \frac{2 (5 \cdot (0))}{2 \cdot 0 + 2 \cdot - 1}$

Step 3.3.1.2.3

Factor $2$ out of $2 \cdot 0 + 2 \cdot - 1$ .

$y = \frac{2 (5 \cdot (0))}{2 \cdot (0 - 1)}$

Step 3.3.1.2.4

Cancel the common factor.

$y = \frac{2 (5 \cdot (0))}{2 \cdot (0 - 1)}$

Step 3.3.1.2.5

Rewrite the expression.

$y = \frac{5 \cdot (0)}{0 - 1}$

Step 3.3.2

Multiply $5$ by $0$ .

$y = \frac{0}{0 - 1}$

Step 3.3.3

Simplify the expression.

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Step 3.3.3.1

Subtract $1$ from $0$ .

$y = \frac{0}{- 1}$

Step 3.3.3.2

Divide $0$ by $- 1$ .

$y = 0$

Step 3.4

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

$(0, 0)$

Step 4

Choose $1$ to substitute in for $x$ to find the ordered pair.

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Step 4.1

Remove parentheses.

$y = \frac{5 (1)}{1 - 2}$

Step 4.2

Remove parentheses.

$y = \frac{5 (1)}{(1) - 2}$

Step 4.3

Simplify $\frac{5 (1)}{(1) - 2}$ .

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Step 4.3.1

Multiply $5$ by $1$ .

$y = \frac{5}{1 - 2}$

Step 4.3.2

Subtract $2$ from $1$ .

$y = \frac{5}{- 1}$

Step 4.3.3

Divide $5$ by $- 1$ .

$y = - 5$

Step 4.4

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

$(1, - 5)$

Step 5

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

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Step 5.1

Remove parentheses.

$y = \frac{5 (3)}{3 - 2}$

Step 5.2

Remove parentheses.

$y = \frac{5 (3)}{(3) - 2}$

Step 5.3

Simplify $\frac{5 (3)}{(3) - 2}$ .

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Step 5.3.1

Multiply $5$ by $3$ .

$y = \frac{15}{3 - 2}$

Step 5.3.2

Subtract $2$ from $3$ .

$y = \frac{15}{1}$

Step 5.3.3

Divide $15$ by $1$ .

$y = 15$

Step 5.4

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

$(3, 15)$

Step 6

These are three possible solutions to the equation.

$(0, 0), (1, - 5), (3, 15)$

Step 7