Algebra Examples

$f (x) = \frac{6 x + 12}{x^{2} + x - 12}$

Step 1

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

$y = \frac{6 (- 2) + 12}{{(- 2)}^{2} - 2 - 12}$

Step 2

Solve the equation for $y$ .

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Step 2.1

Remove parentheses.

$y = \frac{6 (- 2) + 12}{{(- 2)}^{2} - 2 - 12}$

Step 2.2

Simplify $\frac{6 (- 2) + 12}{{(- 2)}^{2} - 2 - 12}$ .

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Step 2.2.1

Simplify the numerator.

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Step 2.2.1.1

Multiply $6$ by $- 2$ .

$y = \frac{- 12 + 12}{{(- 2)}^{2} - 2 - 12}$

Step 2.2.1.2

Add $- 12$ and $12$ .

$y = \frac{0}{{(- 2)}^{2} - 2 - 12}$

Step 2.2.2

Simplify the denominator.

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Step 2.2.2.1

Raise $- 2$ to the power of $2$ .

$y = \frac{0}{4 - 2 - 12}$

Step 2.2.2.2

Subtract $2$ from $4$ .

$y = \frac{0}{2 - 12}$

Step 2.2.2.3

Subtract $12$ from $2$ .

$y = \frac{0}{- 10}$

Step 2.2.3

Divide $0$ by $- 10$ .

$y = 0$

Step 3

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

$y = \frac{6 (- 1) + 12}{{(- 1)}^{2} - 1 - 12}$

Step 4

Solve the equation for $y$ .

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Step 4.1

Remove parentheses.

$y = \frac{6 (- 1) + 12}{{(- 1)}^{2} - 1 - 12}$

Step 4.2

Simplify $\frac{6 (- 1) + 12}{{(- 1)}^{2} - 1 - 12}$ .

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Step 4.2.1

Simplify the numerator.

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Step 4.2.1.1

Multiply $6$ by $- 1$ .

$y = \frac{- 6 + 12}{{(- 1)}^{2} - 1 - 12}$

Step 4.2.1.2

Add $- 6$ and $12$ .

$y = \frac{6}{{(- 1)}^{2} - 1 - 12}$

Step 4.2.2

Simplify the denominator.

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Step 4.2.2.1

Raise $- 1$ to the power of $2$ .

$y = \frac{6}{1 - 1 - 12}$

Step 4.2.2.2

Subtract $1$ from $1$ .

$y = \frac{6}{0 - 12}$

Step 4.2.2.3

Subtract $12$ from $0$ .

$y = \frac{6}{- 12}$

Step 4.2.3

Reduce the expression by cancelling the common factors.

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Step 4.2.3.1

Cancel the common factor of $6$ and $- 12$ .

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Step 4.2.3.1.1

Factor $6$ out of $6$ .

$y = \frac{6 (1)}{- 12}$

Step 4.2.3.1.2

Cancel the common factors.

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Step 4.2.3.1.2.1

Factor $6$ out of $- 12$ .

$y = \frac{6 \cdot 1}{6 \cdot - 2}$

Step 4.2.3.1.2.2

Cancel the common factor.

$y = \frac{6 \cdot 1}{6 \cdot - 2}$

Step 4.2.3.1.2.3

Rewrite the expression.

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

Step 4.2.3.2

Move the negative in front of the fraction.

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

Step 5

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

$y = \frac{6 (0) + 12}{{(0)}^{2} + 0 - 12}$

Step 6

Solve the equation for $y$ .

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Step 6.1

Remove parentheses.

$y = \frac{6 (0) + 12}{{(0)}^{2} + 0 - 12}$

Step 6.2

Remove parentheses.

$y = \frac{6 (0) + 12}{0^{2} + 0 - 12}$

Step 6.3

Remove parentheses.

$y = \frac{6 (0) + 12}{{(0)}^{2} + 0 - 12}$

Step 6.4

Simplify $\frac{6 (0) + 12}{{(0)}^{2} + 0 - 12}$ .

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Step 6.4.1

Simplify the numerator.

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Step 6.4.1.1

Multiply $6$ by $0$ .

$y = \frac{0 + 12}{0^{2} + 0 - 12}$

Step 6.4.1.2

Add $0$ and $12$ .

$y = \frac{12}{0^{2} + 0 - 12}$

Step 6.4.2

Simplify the denominator.

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Step 6.4.2.1

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

$y = \frac{12}{0 + 0 - 12}$

Step 6.4.2.2

Add $0$ and $0$ .

$y = \frac{12}{0 - 12}$

Step 6.4.2.3

Subtract $12$ from $0$ .

$y = \frac{12}{- 12}$

Step 6.4.3

Divide $12$ by $- 12$ .

$y = - 1$

Step 7

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

$y = \frac{6 (1) + 12}{{(1)}^{2} + 1 - 12}$

Step 8

Solve the equation for $y$ .

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Step 8.1

Remove parentheses.

$y = \frac{6 (1) + 12}{{(1)}^{2} + 1 - 12}$

Step 8.2

Remove parentheses.

$y = \frac{6 (1) + 12}{1^{2} + 1 - 12}$

Step 8.3

Remove parentheses.

$y = \frac{6 (1) + 12}{{(1)}^{2} + 1 - 12}$

Step 8.4

Simplify $\frac{6 (1) + 12}{{(1)}^{2} + 1 - 12}$ .

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Step 8.4.1

Simplify the numerator.

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Step 8.4.1.1

Multiply $6$ by $1$ .

$y = \frac{6 + 12}{1^{2} + 1 - 12}$

Step 8.4.1.2

Add $6$ and $12$ .

$y = \frac{18}{1^{2} + 1 - 12}$

Step 8.4.2

Simplify the denominator.

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Step 8.4.2.1

One to any power is one.

$y = \frac{18}{1 + 1 - 12}$

Step 8.4.2.2

Add $1$ and $1$ .

$y = \frac{18}{2 - 12}$

Step 8.4.2.3

Subtract $12$ from $2$ .

$y = \frac{18}{- 10}$

Step 8.4.3

Reduce the expression by cancelling the common factors.

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Step 8.4.3.1

Cancel the common factor of $18$ and $- 10$ .

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Step 8.4.3.1.1

Factor $2$ out of $18$ .

$y = \frac{2 (9)}{- 10}$

Step 8.4.3.1.2

Cancel the common factors.

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Step 8.4.3.1.2.1

Factor $2$ out of $- 10$ .

$y = \frac{2 \cdot 9}{2 \cdot - 5}$

Step 8.4.3.1.2.2

Cancel the common factor.

$y = \frac{2 \cdot 9}{2 \cdot - 5}$

Step 8.4.3.1.2.3

Rewrite the expression.

$y = \frac{9}{- 5}$

Step 8.4.3.2

Move the negative in front of the fraction.

$y = - \frac{9}{5}$

Step 9

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

$y = \frac{6 (2) + 12}{{(2)}^{2} + 2 - 12}$

Step 10

Solve the equation for $y$ .

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Step 10.1

Remove parentheses.

$y = \frac{6 (2) + 12}{{(2)}^{2} + 2 - 12}$

Step 10.2

Remove parentheses.

$y = \frac{6 (2) + 12}{2^{2} + 2 - 12}$

Step 10.3

Remove parentheses.

$y = \frac{6 (2) + 12}{{(2)}^{2} + 2 - 12}$

Step 10.4

Simplify $\frac{6 (2) + 12}{{(2)}^{2} + 2 - 12}$ .

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Step 10.4.1

Cancel the common factor of $6 (2) + 12$ and ${(2)}^{2} + 2 - 12$ .

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Step 10.4.1.1

Factor $2$ out of $6 (2)$ .

$y = \frac{2 (3 \cdot 2) + 12}{{(2)}^{2} + 2 - 12}$

Step 10.4.1.2

Factor $2$ out of $12$ .

$y = \frac{2 (3 \cdot 2) + 2 \cdot 6}{2^{2} + 2 - 12}$

Step 10.4.1.3

Factor $2$ out of $2 (3 \cdot 2) + 2 (6)$ .

$y = \frac{2 (3 \cdot 2 + 6)}{{(2)}^{2} + 2 - 12}$

Step 10.4.1.4

Cancel the common factors.

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Step 10.4.1.4.1

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

$y = \frac{2 (3 \cdot 2 + 6)}{2 \cdot 2 + 2 - 12}$

Step 10.4.1.4.2

Factor $2$ out of $2$ .

$y = \frac{2 (3 \cdot 2 + 6)}{2 \cdot 2 + 2 (1) - 12}$

Step 10.4.1.4.3

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

$y = \frac{2 (3 \cdot 2 + 6)}{2 \cdot (2 + 1) - 12}$

Step 10.4.1.4.4

Factor $2$ out of $- 12$ .

$y = \frac{2 (3 \cdot 2 + 6)}{2 \cdot (2 + 1) + 2 (- 6)}$

Step 10.4.1.4.5

Factor $2$ out of $2 \cdot (2 + 1) + 2 (- 6)$ .

$y = \frac{2 (3 \cdot 2 + 6)}{2 \cdot (2 + 1 - 6)}$

Step 10.4.1.4.6

Cancel the common factor.

$y = \frac{2 (3 \cdot 2 + 6)}{2 \cdot (2 + 1 - 6)}$

Step 10.4.1.4.7

Rewrite the expression.

$y = \frac{3 \cdot 2 + 6}{2 + 1 - 6}$

Step 10.4.2

Simplify the numerator.

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Step 10.4.2.1

Multiply $3$ by $2$ .

$y = \frac{6 + 6}{2 + 1 - 6}$

Step 10.4.2.2

Add $6$ and $6$ .

$y = \frac{12}{2 + 1 - 6}$

Step 10.4.3

Simplify the denominator.

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Step 10.4.3.1

Add $2$ and $1$ .

$y = \frac{12}{3 - 6}$

Step 10.4.3.2

Subtract $6$ from $3$ .

$y = \frac{12}{- 3}$

Step 10.4.4

Divide $12$ by $- 3$ .

$y = - 4$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & 0 \\ - 1 & - \frac{1}{2} \\ 0 & - 1 \\ 1 & - \frac{9}{5} \\ 2 & - 4 \end{array}$

Step 12