Algebra Examples

$f (x) = \frac{x - 2}{x^{2} + 3 x + 2}$

Step 1

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

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

Step 2

Solve the equation for $y$ .

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Step 2.1

Remove parentheses.

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

Step 2.2

Remove parentheses.

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

Step 2.3

Remove parentheses.

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

Step 2.4

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

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Step 2.4.1

Subtract $2$ from $0$ .

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

Step 2.4.2

Simplify the denominator.

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Step 2.4.2.1

Raising $0$ to any positive power yields $0$ .

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

Step 2.4.2.2

Multiply $3$ by $0$ .

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

Step 2.4.2.3

Add $0$ and $0$ .

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

Step 2.4.2.4

Add $0$ and $2$ .

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

Step 2.4.3

Divide $- 2$ by $2$ .

$y = - 1$

Step 3

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

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

Step 4

Solve the equation for $y$ .

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Step 4.1

Remove parentheses.

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

Step 4.2

Remove parentheses.

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

Step 4.3

Remove parentheses.

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

Step 4.4

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

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Step 4.4.1

Subtract $2$ from $1$ .

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

Step 4.4.2

Simplify the denominator.

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Step 4.4.2.1

One to any power is one.

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

Step 4.4.2.2

Multiply $3$ by $1$ .

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

Step 4.4.2.3

Add $1$ and $3$ .

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

Step 4.4.2.4

Add $4$ and $2$ .

$y = \frac{- 1}{6}$

Step 4.4.3

Move the negative in front of the fraction.

$y = - \frac{1}{6}$

Step 5

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

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

Step 6

Solve the equation for $y$ .

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Step 6.1

Remove parentheses.

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

Step 6.2

Remove parentheses.

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

Step 6.3

Remove parentheses.

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

Step 6.4

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

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Step 6.4.1

Reduce the expression by cancelling the common factors.

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Step 6.4.1.1

Cancel the common factor of $(2) - 2$ and ${(2)}^{2} + 3 (2) + 2$ .

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Step 6.4.1.1.1

Factor $2$ out of $2$ .

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

Step 6.4.1.1.2

Factor $2$ out of $- 2$ .

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

Step 6.4.1.1.3

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

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

Step 6.4.1.1.4

Cancel the common factors.

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Step 6.4.1.1.4.1

Factor $2$ out of ${(2)}^{2}$ .

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

Step 6.4.1.1.4.2

Factor $2$ out of $3 (2)$ .

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

Step 6.4.1.1.4.3

Factor $2$ out of $2 \cdot 2 + 2 \cdot 3$ .

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

Step 6.4.1.1.4.4

Factor $2$ out of $2$ .

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

Step 6.4.1.1.4.5

Factor $2$ out of $2 \cdot (2 + 3) + 2 (1)$ .

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

Step 6.4.1.1.4.6

Cancel the common factor.

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

Step 6.4.1.1.4.7

Rewrite the expression.

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

Step 6.4.1.2

Subtract $1$ from $1$ .

$y = \frac{0}{2 + 3 + 1}$

Step 6.4.2

Simplify the denominator.

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Step 6.4.2.1

Add $2$ and $3$ .

$y = \frac{0}{5 + 1}$

Step 6.4.2.2

Add $5$ and $1$ .

$y = \frac{0}{6}$

Step 6.4.3

Divide $0$ by $6$ .

$y = 0$

Step 7

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

$\begin{array}{c} x & y \\ 0 & - 1 \\ 1 & - \frac{1}{6} \\ 2 & 0 \end{array}$

Step 8