Algebra Examples

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

Step 1

Substitute $- 2$ for $x$ and find the result for $y$ .

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

Step 2

Solve the equation for $y$ .

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Step 2.1

Remove parentheses.

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

Step 2.2

Remove parentheses.

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

Step 2.3

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

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Step 2.3.1

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

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Step 2.3.1.1

Factor $2$ out of $- 2$ .

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

Step 2.3.1.2

Cancel the common factors.

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Step 2.3.1.2.1

Factor $2$ out of $- 2$ .

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

Step 2.3.1.2.2

Factor $2$ out of $- 2$ .

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

Step 2.3.1.2.3

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

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

Step 2.3.1.2.4

Cancel the common factor.

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

Step 2.3.1.2.5

Rewrite the expression.

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

Step 2.3.2

Subtract $1$ from $- 1$ .

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

Step 2.3.3

Dividing two negative values results in a positive value.

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

Step 3

Substitute $- 1$ for $x$ and find the result for $y$ .

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

Step 4

Solve the equation for $y$ .

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Step 4.1

Remove parentheses.

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

Step 4.2

Remove parentheses.

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

Step 4.3

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

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Step 4.3.1

Subtract $2$ from $- 1$ .

$y = \frac{- 1}{- 3}$

Step 4.3.2

Dividing two negative values results in a positive value.

$y = \frac{1}{3}$

Step 5

Substitute $0$ for $x$ and find the result for $y$ .

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

Step 6

Solve the equation for $y$ .

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Step 6.1

Remove parentheses.

$y = \frac{0}{0 - 2}$

Step 6.2

Remove parentheses.

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

Step 6.3

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

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Step 6.3.1

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

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Step 6.3.1.1

Factor $2$ out of $0$ .

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

Step 6.3.1.2

Cancel the common factors.

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Step 6.3.1.2.1

Factor $2$ out of $0$ .

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

Step 6.3.1.2.2

Factor $2$ out of $- 2$ .

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

Step 6.3.1.2.3

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

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

Step 6.3.1.2.4

Cancel the common factor.

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

Step 6.3.1.2.5

Rewrite the expression.

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

Step 6.3.2

Simplify the expression.

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Step 6.3.2.1

Subtract $1$ from $0$ .

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

Step 6.3.2.2

Divide $0$ by $- 1$ .

$y = 0$

Step 7

Substitute $1$ for $x$ and find the result for $y$ .

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

Step 8

Solve the equation for $y$ .

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Step 8.1

Remove parentheses.

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

Step 8.2

Remove parentheses.

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

Step 8.3

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

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Step 8.3.1

Subtract $2$ from $1$ .

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

Step 8.3.2

Divide $1$ by $- 1$ .

$y = - 1$

Step 9

This is a table of possible values to use when graphing the equation.

$\begin{array}{c} x & y \\ - 2 & \frac{1}{2} \\ - 1 & \frac{1}{3} \\ 0 & 0 \\ 1 & - 1 \end{array}$

Step 10