Algebra Examples

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

Step 1

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

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

Step 2

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

Tap for more steps...

Step 2.1

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 2.1.1

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

Tap for more steps...

Step 2.1.1.1

Factor $2$ out of $- 2$ .

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

Step 2.1.1.2

Factor $2$ out of $2 (- 2) + 2 (- 1)$ .

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

Step 2.1.1.3

Cancel the common factors.

Tap for more steps...

Step 2.1.1.3.1

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

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

Step 2.1.1.3.2

Factor $2$ out of $4$ .

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

Step 2.1.1.3.3

Factor $2$ out of $2 (- (- 1)) + 2 (2)$ .

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

Step 2.1.1.3.4

Cancel the common factor.

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

Step 2.1.1.3.5

Rewrite the expression.

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

Step 2.1.2

Subtract $1$ from $- 2$ .

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

Step 2.2

Simplify the denominator.

Tap for more steps...

Step 2.2.1

Multiply $- 1$ by $- 1$ .

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

Step 2.2.2

Add $1$ and $2$ .

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

Step 2.3

Divide $- 3$ by $3$ .

$y = - 1$

Step 3

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

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

Step 4

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

Tap for more steps...

Step 4.1

Simplify the numerator.

Tap for more steps...

Step 4.1.1

Multiply $2$ by $- 1$ .

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

Step 4.1.2

Subtract $2$ from $- 2$ .

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

Step 4.2

Simplify the denominator.

Tap for more steps...

Step 4.2.1

Multiply $- 1$ by $- 1$ .

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

Step 4.2.2

Add $1$ and $4$ .

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

Step 4.3

Move the negative in front of the fraction.

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

Step 5

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

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

Step 6

Solve the equation for $y$ .

Tap for more steps...

Step 6.1

Remove parentheses.

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

Step 6.2

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

Tap for more steps...

Step 6.2.1

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

Tap for more steps...

Step 6.2.1.1

Factor $- 1$ out of $2 (0)$ .

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

Step 6.2.1.2

Rewrite $- 2$ as $- 1 (2)$ .

$y = \frac{- (- 2 \cdot 0) - 1 (2)}{- (0) + 4}$

Step 6.2.1.3

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

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

Step 6.2.1.4

Rewrite $- (- 2 \cdot 0 + 2)$ as $- 1 (- 2 \cdot 0 + 2)$ .

$y = \frac{- 1 (- 2 \cdot 0 + 2)}{- (0) + 4}$

Step 6.2.1.5

Reorder terms.

$y = \frac{- 1 (2 - 2 \cdot 0)}{- (0) + 4}$

Step 6.2.1.6

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

$y = \frac{2 (- 1 (1 - 0))}{- (0) + 4}$

Step 6.2.1.7

Cancel the common factors.

Tap for more steps...

Step 6.2.1.7.1

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

$y = \frac{2 (- 1 (1 - 0))}{2 (- (0)) + 4}$

Step 6.2.1.7.2

Factor $2$ out of $4$ .

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

Step 6.2.1.7.3

Factor $2$ out of $2 (- (0)) + 2 (2)$ .

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

Step 6.2.1.7.4

Cancel the common factor.

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

Step 6.2.1.7.5

Rewrite the expression.

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

Step 6.2.2

Simplify the numerator.

Tap for more steps...

Step 6.2.2.1

Multiply $- 1$ by $0$ .

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

Step 6.2.2.2

Add $1$ and $0$ .

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

Step 6.2.3

Simplify the denominator.

Tap for more steps...

Step 6.2.3.1

Multiply $- 1$ by $0$ .

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

Step 6.2.3.2

Add $0$ and $2$ .

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

Step 6.2.4

Simplify the expression.

Tap for more steps...

Step 6.2.4.1

Multiply $- 1$ by $1$ .

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

Step 6.2.4.2

Move the negative in front of the fraction.

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

Step 7

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

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

Step 8

Solve the equation for $y$ .

Tap for more steps...

Step 8.1

Remove parentheses.

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

Step 8.2

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

Tap for more steps...

Step 8.2.1

Simplify the numerator.

Tap for more steps...

Step 8.2.1.1

Multiply $2$ by $1$ .

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

Step 8.2.1.2

Subtract $2$ from $2$ .

$y = \frac{0}{- (1) + 4}$

Step 8.2.2

Simplify the denominator.

Tap for more steps...

Step 8.2.2.1

Multiply $- 1$ by $1$ .

$y = \frac{0}{- 1 + 4}$

Step 8.2.2.2

Add $- 1$ and $4$ .

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

Step 8.2.3

Divide $0$ by $3$ .

$y = 0$

Step 9

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

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

Step 10

Solve the equation for $y$ .

Tap for more steps...

Step 10.1

Remove parentheses.

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

Step 10.2

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

Tap for more steps...

Step 10.2.1

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

Tap for more steps...

Step 10.2.1.1

Factor $2$ out of $- 2$ .

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

Step 10.2.1.2

Factor $2$ out of $2 (2) + 2 (- 1)$ .

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

Step 10.2.1.3

Cancel the common factors.

Tap for more steps...

Step 10.2.1.3.1

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

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

Step 10.2.1.3.2

Factor $2$ out of $4$ .

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

Step 10.2.1.3.3

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

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

Step 10.2.1.3.4

Cancel the common factor.

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

Step 10.2.1.3.5

Rewrite the expression.

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

Step 10.2.2

Simplify the expression.

Tap for more steps...

Step 10.2.2.1

Subtract $1$ from $2$ .

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

Step 10.2.2.2

Add $- 1$ and $2$ .

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

Step 10.2.2.3

Divide $1$ by $1$ .

$y = 1$

Step 11

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

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

Step 12