Algebra Examples

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

Step 1

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

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

Step 2

Solve the equation for $y$ .

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Step 2.1

Remove parentheses.

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

Step 2.2

Remove parentheses.

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

Step 2.3

Remove parentheses.

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

Step 2.4

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

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Step 2.4.1

Subtract $2$ from $- 1$ .

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

Step 2.4.2

Add $- 1$ and $2$ .

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

Step 2.4.3

Divide $- 3$ by $1$ .

$y = - 3$

Step 3

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

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

Step 4

Solve the equation for $y$ .

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Step 4.1

Remove parentheses.

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

Step 4.2

Remove parentheses.

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

Step 4.3

Remove parentheses.

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

Step 4.4

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

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Step 4.4.1

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

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Step 4.4.1.1

Factor $2$ out of $0$ .

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

Step 4.4.1.2

Factor $2$ out of $- 2$ .

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

Step 4.4.1.3

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

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

Step 4.4.1.4

Cancel the common factors.

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Step 4.4.1.4.1

Factor $2$ out of $0$ .

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

Step 4.4.1.4.2

Factor $2$ out of $2$ .

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

Step 4.4.1.4.3

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

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

Step 4.4.1.4.4

Cancel the common factor.

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

Step 4.4.1.4.5

Rewrite the expression.

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

Step 4.4.2

Cancel the common factor of $0 - 1$ and $0 + 1$ .

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Step 4.4.2.1

Rewrite $0$ as $- 1 (0)$ .

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

Step 4.4.2.2

Rewrite $- 1$ as $- 1 (1)$ .

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

Step 4.4.2.3

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

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

Step 4.4.2.4

Cancel the common factor.

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

Step 4.4.2.5

Divide $- 1$ by $1$ .

$y = - 1$

Step 5

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

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

Step 6

Solve the equation for $y$ .

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Step 6.1

Remove parentheses.

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

Step 6.2

Remove parentheses.

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

Step 6.3

Remove parentheses.

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

Step 6.4

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

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Step 6.4.1

Subtract $2$ from $1$ .

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

Step 6.4.2

Add $1$ and $2$ .

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

Step 6.4.3

Move the negative in front of the fraction.

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

Step 7

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

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

Step 8

Solve the equation for $y$ .

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Step 8.1

Remove parentheses.

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

Step 8.2

Remove parentheses.

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

Step 8.3

Remove parentheses.

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

Step 8.4

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

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Step 8.4.1

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

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Step 8.4.1.1

Factor $2$ out of $2$ .

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

Step 8.4.1.2

Factor $2$ out of $- 2$ .

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

Step 8.4.1.3

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

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

Step 8.4.1.4

Cancel the common factors.

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Step 8.4.1.4.1

Factor $2$ out of $2$ .

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

Step 8.4.1.4.2

Factor $2$ out of $2$ .

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

Step 8.4.1.4.3

Factor $2$ out of $2 \cdot 1 + 2 (1)$ .

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

Step 8.4.1.4.4

Cancel the common factor.

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

Step 8.4.1.4.5

Rewrite the expression.

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

Step 8.4.2

Simplify the expression.

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Step 8.4.2.1

Subtract $1$ from $1$ .

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

Step 8.4.2.2

Add $1$ and $1$ .

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

Step 8.4.2.3

Divide $0$ by $2$ .

$y = 0$

Step 9

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

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

Step 10