Algebra Examples

$f (x) = \frac{4 x + 6}{x + 2}$

Step 1

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

$y = \frac{4 (- 1) + 6}{(- 1) + 2}$

Step 2

Solve the equation for $y$ .

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Step 2.1

Remove parentheses.

$y = \frac{4 (- 1) + 6}{- 1 + 2}$

Step 2.2

Remove parentheses.

$y = \frac{4 (- 1) + 6}{(- 1) + 2}$

Step 2.3

Simplify $\frac{4 (- 1) + 6}{(- 1) + 2}$ .

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Step 2.3.1

Simplify the numerator.

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Step 2.3.1.1

Multiply $4$ by $- 1$ .

$y = \frac{- 4 + 6}{- 1 + 2}$

Step 2.3.1.2

Add $- 4$ and $6$ .

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

Step 2.3.2

Simplify the expression.

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Step 2.3.2.1

Add $- 1$ and $2$ .

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

Step 2.3.2.2

Divide $2$ by $1$ .

$y = 2$

Step 3

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

$y = \frac{4 (0) + 6}{(0) + 2}$

Step 4

Solve the equation for $y$ .

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Step 4.1

Remove parentheses.

$y = \frac{4 (0) + 6}{0 + 2}$

Step 4.2

Remove parentheses.

$y = \frac{4 (0) + 6}{(0) + 2}$

Step 4.3

Simplify $\frac{4 (0) + 6}{(0) + 2}$ .

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Step 4.3.1

Cancel the common factor of $4 (0) + 6$ and $(0) + 2$ .

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Step 4.3.1.1

Factor $2$ out of $4 (0)$ .

$y = \frac{2 (2 \cdot 0) + 6}{(0) + 2}$

Step 4.3.1.2

Factor $2$ out of $6$ .

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

Step 4.3.1.3

Factor $2$ out of $2 (2 \cdot 0) + 2 (3)$ .

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

Step 4.3.1.4

Cancel the common factors.

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Step 4.3.1.4.1

Factor $2$ out of $0$ .

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

Step 4.3.1.4.2

Factor $2$ out of $2$ .

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

Step 4.3.1.4.3

Factor $2$ out of $2 \cdot 0 + 2 \cdot 1$ .

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

Step 4.3.1.4.4

Cancel the common factor.

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

Step 4.3.1.4.5

Rewrite the expression.

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

Step 4.3.2

Simplify the numerator.

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Step 4.3.2.1

Multiply $2$ by $0$ .

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

Step 4.3.2.2

Add $0$ and $3$ .

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

Step 4.3.3

Simplify the expression.

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Step 4.3.3.1

Add $0$ and $1$ .

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

Step 4.3.3.2

Divide $3$ by $1$ .

$y = 3$

Step 5

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

$y = \frac{4 (1) + 6}{(1) + 2}$

Step 6

Solve the equation for $y$ .

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Step 6.1

Remove parentheses.

$y = \frac{4 (1) + 6}{1 + 2}$

Step 6.2

Remove parentheses.

$y = \frac{4 (1) + 6}{(1) + 2}$

Step 6.3

Simplify $\frac{4 (1) + 6}{(1) + 2}$ .

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Step 6.3.1

Simplify the numerator.

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Step 6.3.1.1

Multiply $4$ by $1$ .

$y = \frac{4 + 6}{1 + 2}$

Step 6.3.1.2

Add $4$ and $6$ .

$y = \frac{10}{1 + 2}$

Step 6.3.2

Add $1$ and $2$ .

$y = \frac{10}{3}$

Step 7

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

$y = \frac{4 (2) + 6}{(2) + 2}$

Step 8

Solve the equation for $y$ .

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Step 8.1

Remove parentheses.

$y = \frac{4 (2) + 6}{2 + 2}$

Step 8.2

Remove parentheses.

$y = \frac{4 (2) + 6}{(2) + 2}$

Step 8.3

Simplify $\frac{4 (2) + 6}{(2) + 2}$ .

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Step 8.3.1

Cancel the common factor of $4 (2) + 6$ and $(2) + 2$ .

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Step 8.3.1.1

Factor $2$ out of $4 (2)$ .

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

Step 8.3.1.2

Factor $2$ out of $6$ .

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

Step 8.3.1.3

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

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

Step 8.3.1.4

Cancel the common factors.

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Step 8.3.1.4.1

Factor $2$ out of $2$ .

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

Step 8.3.1.4.2

Factor $2$ out of $2$ .

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

Step 8.3.1.4.3

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

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

Step 8.3.1.4.4

Cancel the common factor.

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

Step 8.3.1.4.5

Rewrite the expression.

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

Step 8.3.2

Simplify the numerator.

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Step 8.3.2.1

Multiply $2$ by $2$ .

$y = \frac{4 + 3}{1 + 1}$

Step 8.3.2.2

Add $4$ and $3$ .

$y = \frac{7}{1 + 1}$

Step 8.3.3

Add $1$ and $1$ .

$y = \frac{7}{2}$

Step 9

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

$\begin{array}{c} x & y \\ - 1 & 2 \\ 0 & 3 \\ 1 & \frac{10}{3} \\ 2 & \frac{7}{2} \end{array}$

Step 10