Algebra Examples

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

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

Step 1

Substitute

0

$0$ for

x

$x$ and find the result for

y

$y$ .

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

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

Step 2

Solve the equation for

y

$y$ .

Tap for more steps...

Step 2.1

Remove parentheses.

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

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

Step 2.2

Remove parentheses.

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

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

Step 2.3

Remove parentheses.

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

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

Step 2.4

Simplify

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

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

Tap for more steps...

Step 2.4.1

Subtract

2

$2$ from

0

$0$ .

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

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

Step 2.4.2

Simplify the denominator.

Tap for more steps...

Step 2.4.2.1

Raising

0

$0$ to any positive power yields

0

$0$ .

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

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

Step 2.4.2.2

Multiply

3

$3$ by

0

$0$ .

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

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

Step 2.4.2.3

Add

0

$0$ and

0

$0$ .

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

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

Step 2.4.2.4

Add

0

$0$ and

2

$2$ .

y = \frac{- 2}{2}

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

y = \frac{- 2}{2}

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

Step 2.4.3

Divide

- 2

$- 2$ by

2

$2$ .

y = - 1

$y = - 1$

y = - 1

$y = - 1$

y = - 1

$y = - 1$

Step 3

Substitute

1

$1$ for

x

$x$ and find the result for

y

$y$ .

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

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

Step 4

Solve the equation for

y

$y$ .

Tap for more steps...

Step 4.1

Remove parentheses.

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

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

Step 4.2

Remove parentheses.

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

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

Step 4.3

Remove parentheses.

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

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

Step 4.4

Simplify

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

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

Tap for more steps...

Step 4.4.1

Subtract

2

$2$ from

1

$1$ .

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

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

Step 4.4.2

Simplify the denominator.

Tap for more steps...

Step 4.4.2.1

One to any power is one.

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

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

Step 4.4.2.2

Multiply

3

$3$ by

1

$1$ .

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

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

Step 4.4.2.3

Add

1

$1$ and

3

$3$ .

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

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

Step 4.4.2.4

Add

4

$4$ and

2

$2$ .

y = \frac{- 1}{6}

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

y = \frac{- 1}{6}

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

Step 4.4.3

Move the negative in front of the fraction.

y = - \frac{1}{6}

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

y = - \frac{1}{6}

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

y = - \frac{1}{6}

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

Step 5

Substitute

2

$2$ for

x

$x$ and find the result for

y

$y$ .

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

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

Step 6

Solve the equation for

y

$y$ .

Tap for more steps...

Step 6.1

Remove parentheses.

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

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

Step 6.2

Remove parentheses.

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

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

Step 6.3

Remove parentheses.

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

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

Step 6.4

Simplify

\frac{(2) - 2}{{(2)}^{2} + 3 (2) + 2}

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

Tap for more steps...

Step 6.4.1

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 6.4.1.1

Cancel the common factor of

(2) - 2

$(2) - 2$ and

{(2)}^{2} + 3 (2) + 2

${(2)}^{2} + 3 (2) + 2$ .

Tap for more steps...

Step 6.4.1.1.1

Factor

2

$2$ out of

2

$2$ .

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

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

Step 6.4.1.1.2

Factor

2

$2$ out of

- 2

$- 2$ .

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

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

Step 6.4.1.1.3

Factor

2

$2$ out of

2 \cdot 1 + 2 \cdot - 1

$2 \cdot 1 + 2 \cdot - 1$ .

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

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

Step 6.4.1.1.4

Cancel the common factors.

Tap for more steps...

Step 6.4.1.1.4.1

Factor

2

$2$ out of

{(2)}^{2}

${(2)}^{2}$ .

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

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

Step 6.4.1.1.4.2

Factor

2

$2$ out of

3 (2)

$3 (2)$ .

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

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

Step 6.4.1.1.4.3

Factor

2

$2$ out of

2 \cdot 2 + 2 \cdot 3

$2 \cdot 2 + 2 \cdot 3$ .

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

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

Step 6.4.1.1.4.4

Factor

2

$2$ out of

2

$2$ .

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

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

Step 6.4.1.1.4.5

Factor

2

$2$ out of

2 \cdot (2 + 3) + 2 (1)

$2 \cdot (2 + 3) + 2 (1)$ .

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

Tap for more steps...

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