Algebra Examples

$\frac{4 x - 8}{(x - 4) (x + 1)}$

Step 1

Write $\frac{4 x - 8}{(x - 4) (x + 1)}$ as an equation.

$y = \frac{4 x - 8}{(x - 4) (x + 1)}$

Step 2

Find the x-intercepts.

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Step 2.1

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = \frac{4 x - 8}{(x - 4) (x + 1)}$

Step 2.2

Solve the equation.

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Step 2.2.1

Set the numerator equal to zero.

$4 x - 8 = 0$

Step 2.2.2

Solve the equation for $x$ .

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Step 2.2.2.1

Add $8$ to both sides of the equation.

$4 x = 8$

Step 2.2.2.2

Divide each term in $4 x = 8$ by $4$ and simplify.

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Step 2.2.2.2.1

Divide each term in $4 x = 8$ by $4$ .

$\frac{4 x}{4} = \frac{8}{4}$

Step 2.2.2.2.2

Simplify the left side.

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Step 2.2.2.2.2.1

Cancel the common factor of $4$ .

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Step 2.2.2.2.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{8}{4}$

Step 2.2.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{8}{4}$

Step 2.2.2.2.3

Simplify the right side.

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Step 2.2.2.2.3.1

Divide $8$ by $4$ .

$x = 2$

Step 2.3

x-intercept(s) in point form.

x-intercept(s): $(2, 0)$

Step 3

Find the y-intercepts.

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Step 3.1

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = \frac{4 (0) - 8}{((0) - 4) ((0) + 1)}$

Step 3.2

Solve the equation.

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Step 3.2.1

Remove parentheses.

$y = \frac{4 (0) - 8}{(0 - 4) ((0) + 1)}$

Step 3.2.2

Remove parentheses.

$y = \frac{4 (0) - 8}{(0 - 4) (0 + 1)}$

Step 3.2.3

Remove parentheses.

$y = \frac{4 (0) - 8}{((0) - 4) ((0) + 1)}$

Step 3.2.4

Simplify $\frac{4 (0) - 8}{((0) - 4) ((0) + 1)}$ .

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Step 3.2.4.1

Reduce the expression by cancelling the common factors.

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Step 3.2.4.1.1

Cancel the common factor of $4 (0) - 8$ and $(0) - 4$ .

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Step 3.2.4.1.1.1

Factor $4$ out of $- 8$ .

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

Step 3.2.4.1.1.2

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

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

Step 3.2.4.1.1.3

Cancel the common factors.

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Step 3.2.4.1.1.3.1

Factor $4$ out of $((0) - 4) ((0) + 1)$ .

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

Step 3.2.4.1.1.3.2

Cancel the common factor.

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

Step 3.2.4.1.1.3.3

Rewrite the expression.

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

Step 3.2.4.1.2

Subtract $2$ from $0$ .

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

Step 3.2.4.2

Simplify the denominator.

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Step 3.2.4.2.1

Rewrite $0$ as $- 1 (0)$ .

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

Step 3.2.4.2.2

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

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

Step 3.2.4.2.3

Factor $- 1$ out of $- 1 \cdot 0 - 1 \cdot 1$ .

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

Step 3.2.4.2.4

Raise $0 + 1$ to the power of $1$ .

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

Step 3.2.4.2.5

Raise $0 + 1$ to the power of $1$ .

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

Step 3.2.4.2.6

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 3.2.4.2.7

Add $1$ and $1$ .

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

Step 3.2.4.3

Simplify the denominator.

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Step 3.2.4.3.1

Add $0$ and $1$ .

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

Step 3.2.4.3.2

One to any power is one.

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

Step 3.2.4.4

Simplify the expression.

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Step 3.2.4.4.1

Multiply $- 1$ by $1$ .

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

Step 3.2.4.4.2

Divide $- 2$ by $- 1$ .

$y = 2$

Step 3.3

y-intercept(s) in point form.

y-intercept(s): $(0, 2)$

Step 4

List the intersections.

x-intercept(s): $(2, 0)$

y-intercept(s): $(0, 2)$

Step 5