Algebra Examples

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

Step 1

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

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

Step 2

Solve the equation for $y$ .

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Step 2.1

Remove parentheses.

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

Step 2.2

Remove parentheses.

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

Step 2.3

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

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Step 2.3.1

Subtract $3$ from $- 2$ .

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

Step 2.3.2

Move the negative in front of the fraction.

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

Step 3

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

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

Step 4

Solve the equation for $y$ .

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Step 4.1

Remove parentheses.

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

Step 4.2

Remove parentheses.

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

Step 4.3

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

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Step 4.3.1

Subtract $3$ from $- 1$ .

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

Step 4.3.2

Move the negative in front of the fraction.

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

Step 5

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

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

Step 6

Solve the equation for $y$ .

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Step 6.1

Remove parentheses.

$y = \frac{1}{0 - 3}$

Step 6.2

Remove parentheses.

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

Step 6.3

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

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Step 6.3.1

Subtract $3$ from $0$ .

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

Step 6.3.2

Move the negative in front of the fraction.

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

Step 7

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

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

Step 8

Solve the equation for $y$ .

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Step 8.1

Remove parentheses.

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

Step 8.2

Remove parentheses.

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

Step 8.3

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

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Step 8.3.1

Subtract $3$ from $1$ .

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

Step 8.3.2

Move the negative in front of the fraction.

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

Step 9

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

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

Step 10

Solve the equation for $y$ .

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Step 10.1

Remove parentheses.

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

Step 10.2

Remove parentheses.

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

Step 10.3

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

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Step 10.3.1

Subtract $3$ from $2$ .

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

Step 10.3.2

Divide $1$ by $- 1$ .

$y = - 1$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & - \frac{1}{5} \\ - 1 & - \frac{1}{4} \\ 0 & - \frac{1}{3} \\ 1 & - \frac{1}{2} \\ 2 & - 1 \end{array}$

Step 12