Algebra Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

Simplify the numerator.

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Step 2.1.1

Multiply $2$ by $- 2$ .

$y = \frac{- 4 - 3}{- (- 2) + 3}$

Step 2.1.2

Subtract $3$ from $- 4$ .

$y = \frac{- 7}{- (- 2) + 3}$

Step 2.2

Simplify the denominator.

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Step 2.2.1

Multiply $- 1$ by $- 2$ .

$y = \frac{- 7}{2 + 3}$

Step 2.2.2

Add $2$ and $3$ .

$y = \frac{- 7}{5}$

Step 2.3

Move the negative in front of the fraction.

$y = - \frac{7}{5}$

Step 3

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

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

Step 4

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

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Multiply $2$ by $- 1$ .

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

Step 4.1.2

Subtract $3$ from $- 2$ .

$y = \frac{- 5}{- (- 1) + 3}$

Step 4.2

Simplify the denominator.

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Step 4.2.1

Multiply $- 1$ by $- 1$ .

$y = \frac{- 5}{1 + 3}$

Step 4.2.2

Add $1$ and $3$ .

$y = \frac{- 5}{4}$

Step 4.3

Move the negative in front of the fraction.

$y = - \frac{5}{4}$

Step 5

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

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

Step 6

Solve the equation for $y$ .

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Step 6.1

Remove parentheses.

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

Step 6.2

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

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Step 6.2.1

Cancel the common factor of $2 (0) - 3$ and $- (0) + 3$ .

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Step 6.2.1.1

Factor $3$ out of $2 (0)$ .

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

Step 6.2.1.2

Factor $3$ out of $- 3$ .

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

Step 6.2.1.3

Factor $3$ out of $3 (2 \cdot (0)) + 3 (- 1)$ .

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

Step 6.2.1.4

Cancel the common factors.

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Step 6.2.1.4.1

Factor $3$ out of $- (0)$ .

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

Step 6.2.1.4.2

Factor $3$ out of $3$ .

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

Step 6.2.1.4.3

Factor $3$ out of $3 (- (0)) + 3 (1)$ .

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

Step 6.2.1.4.4

Cancel the common factor.

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

Step 6.2.1.4.5

Rewrite the expression.

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

Step 6.2.2

Simplify the numerator.

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Step 6.2.2.1

Multiply $2$ by $0$ .

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

Step 6.2.2.2

Subtract $1$ from $0$ .

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

Step 6.2.3

Simplify the denominator.

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Step 6.2.3.1

Multiply $- 1$ by $0$ .

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

Step 6.2.3.2

Add $0$ and $1$ .

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

Step 6.2.4

Divide $- 1$ by $1$ .

$y = - 1$

Step 7

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

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

Step 8

Solve the equation for $y$ .

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Step 8.1

Remove parentheses.

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

Step 8.2

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

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Step 8.2.1

Simplify the numerator.

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Step 8.2.1.1

Multiply $2$ by $1$ .

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

Step 8.2.1.2

Subtract $3$ from $2$ .

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

Step 8.2.2

Simplify the denominator.

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Step 8.2.2.1

Multiply $- 1$ by $1$ .

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

Step 8.2.2.2

Add $- 1$ and $3$ .

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

Step 8.2.3

Move the negative in front of the fraction.

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

Step 9

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

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

Step 10

Solve the equation for $y$ .

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Step 10.1

Remove parentheses.

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

Step 10.2

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

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Step 10.2.1

Simplify the numerator.

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Step 10.2.1.1

Multiply $2$ by $2$ .

$y = \frac{4 - 3}{- (2) + 3}$

Step 10.2.1.2

Subtract $3$ from $4$ .

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

Step 10.2.2

Simplify the denominator.

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Step 10.2.2.1

Multiply $- 1$ by $2$ .

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

Step 10.2.2.2

Add $- 2$ and $3$ .

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

Step 10.2.3

Divide $1$ by $1$ .

$y = 1$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & - \frac{7}{5} \\ - 1 & - \frac{5}{4} \\ 0 & - 1 \\ 1 & - \frac{1}{2} \\ 2 & 1 \end{array}$

Step 12