Algebra Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

Simplify the numerator.

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Step 2.1.1

Multiply $3$ by $- 1$ .

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

Step 2.1.2

Add $- 3$ and $3$ .

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

Step 2.2

Simplify the denominator.

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Step 2.2.1

Multiply $- 1$ by $- 1$ .

$y = \frac{0}{1 - 2}$

Step 2.2.2

Subtract $2$ from $1$ .

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

Step 2.3

Divide $0$ by $- 1$ .

$y = 0$

Step 3

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

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

Step 4

Solve the equation for $y$ .

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Step 4.1

Remove parentheses.

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

Step 4.2

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

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Step 4.2.1

Simplify the numerator.

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Step 4.2.1.1

Multiply $3$ by $0$ .

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

Step 4.2.1.2

Add $0$ and $3$ .

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

Step 4.2.2

Simplify the denominator.

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Step 4.2.2.1

Multiply $- 1$ by $0$ .

$y = \frac{3}{0 - 2}$

Step 4.2.2.2

Subtract $2$ from $0$ .

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

Step 4.2.3

Move the negative in front of the fraction.

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

Step 5

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

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

Step 6

Solve the equation for $y$ .

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Step 6.1

Remove parentheses.

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

Step 6.2

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

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Step 6.2.1

Simplify the numerator.

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Step 6.2.1.1

Multiply $3$ by $1$ .

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

Step 6.2.1.2

Add $3$ and $3$ .

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

Step 6.2.2

Simplify the denominator.

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Step 6.2.2.1

Multiply $- 1$ by $1$ .

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

Step 6.2.2.2

Subtract $2$ from $- 1$ .

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

Step 6.2.3

Divide $6$ by $- 3$ .

$y = - 2$

Step 7

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

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

Step 8

Solve the equation for $y$ .

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Step 8.1

Remove parentheses.

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

Step 8.2

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

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Step 8.2.1

Simplify the numerator.

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Step 8.2.1.1

Multiply $3$ by $2$ .

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

Step 8.2.1.2

Add $6$ and $3$ .

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

Step 8.2.2

Simplify the denominator.

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Step 8.2.2.1

Multiply $- 1$ by $2$ .

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

Step 8.2.2.2

Subtract $2$ from $- 2$ .

$y = \frac{9}{- 4}$

Step 8.2.3

Move the negative in front of the fraction.

$y = - \frac{9}{4}$

Step 9

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

$\begin{array}{c} x & y \\ - 1 & 0 \\ 0 & - \frac{3}{2} \\ 1 & - 2 \\ 2 & - \frac{9}{4} \end{array}$

Step 10