Algebra Examples

$\frac{x^{2} + 2 x}{- 4 x + 8}$

Step 1

Write $\frac{x^{2} + 2 x}{- 4 x + 8}$ as an equation.

$y = \frac{x^{2} + 2 x}{- 4 x + 8}$

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 $x$ .

$0 = \frac{x^{2} + 2 x}{- 4 x + 8}$

Step 2.2

Solve the equation.

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Step 2.2.1

Set the numerator equal to zero.

$x^{2} + 2 x = 0$

Step 2.2.2

Solve the equation for $x$ .

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Step 2.2.2.1

Factor $x$ out of $x^{2} + 2 x$ .

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Step 2.2.2.1.1

Factor $x$ out of $x^{2}$ .

$x \cdot x + 2 x = 0$

Step 2.2.2.1.2

Factor $x$ out of $2 x$ .

$x \cdot x + x \cdot 2 = 0$

Step 2.2.2.1.3

Factor $x$ out of $x \cdot x + x \cdot 2$ .

$x (x + 2) = 0$

Step 2.2.2.2

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$x + 2 = 0$

Step 2.2.2.3

Set $x$ equal to $0$ .

$x = 0$

Step 2.2.2.4

Set $x + 2$ equal to $0$ and solve for $x$ .

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Step 2.2.2.4.1

Set $x + 2$ equal to $0$ .

$x + 2 = 0$

Step 2.2.2.4.2

Subtract $2$ from both sides of the equation.

$x = - 2$

Step 2.2.2.5

The final solution is all the values that make $x (x + 2) = 0$ true.

$x = 0, - 2$

Step 2.3

x-intercept(s) in point form.

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

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 $y$ .

$y = \frac{{(0)}^{2} + 2 (0)}{- 4 \cdot 0 + 8}$

Step 3.2

Solve the equation.

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Step 3.2.1

Remove parentheses.

$y = \frac{0^{2} + 2 (0)}{- 4 \cdot 0 + 8}$

Step 3.2.2

Remove parentheses.

$y = \frac{{(0)}^{2} + 2 (0)}{- 4 \cdot 0 + 8}$

Step 3.2.3

Simplify $\frac{{(0)}^{2} + 2 (0)}{- 4 \cdot 0 + 8}$ .

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Step 3.2.3.1

Simplify the numerator.

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Step 3.2.3.1.1

Raising $0$ to any positive power yields $0$ .

$y = \frac{0 + 2 (0)}{- 4 \cdot 0 + 8}$

Step 3.2.3.1.2

Multiply $2$ by $0$ .

$y = \frac{0 + 0}{- 4 \cdot 0 + 8}$

Step 3.2.3.1.3

Add $0$ and $0$ .

$y = \frac{0}{- 4 \cdot 0 + 8}$

Step 3.2.3.2

Simplify the denominator.

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Step 3.2.3.2.1

Multiply $- 4$ by $0$ .

$y = \frac{0}{0 + 8}$

Step 3.2.3.2.2

Add $0$ and $8$ .

$y = \frac{0}{8}$

Step 3.2.3.3

Divide $0$ by $8$ .

$y = 0$

Step 3.3

y-intercept(s) in point form.

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

Step 4

List the intersections.

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

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

Step 5