Algebra Examples

$\frac{3 x^{2}}{2 x^{2} - 32}$

Step 1

Write $\frac{3 x^{2}}{2 x^{2} - 32}$ as an equation.

$y = \frac{3 x^{2}}{2 x^{2} - 32}$

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 $x$ .

$0 = \frac{3 x^{2}}{2 x^{2} - 32}$

Step 2.2

Solve the equation.

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Step 2.2.1

Set the numerator equal to zero.

$3 x^{2} = 0$

Step 2.2.2

Solve the equation for $x$ .

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Step 2.2.2.1

Divide each term in $3 x^{2} = 0$ by $3$ and simplify.

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Step 2.2.2.1.1

Divide each term in $3 x^{2} = 0$ by $3$ .

$\frac{3 x^{2}}{3} = \frac{0}{3}$

Step 2.2.2.1.2

Simplify the left side.

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Step 2.2.2.1.2.1

Cancel the common factor of $3$ .

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Step 2.2.2.1.2.1.1

Cancel the common factor.

$\frac{3 x^{2}}{3} = \frac{0}{3}$

Step 2.2.2.1.2.1.2

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{0}{3}$

Step 2.2.2.1.3

Simplify the right side.

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Step 2.2.2.1.3.1

Divide $0$ by $3$ .

$x^{2} = 0$

Step 2.2.2.2

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{0}$

Step 2.2.2.3

Simplify $\pm \sqrt{0}$ .

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Step 2.2.2.3.1

Rewrite $0$ as $0^{2}$ .

$x = \pm \sqrt{0^{2}}$

Step 2.2.2.3.2

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 0$

Step 2.2.2.3.3

Plus or minus $0$ is $0$ .

$x = 0$

Step 2.3

x-intercept(s) in point form.

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

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 $y$ .

$y = \frac{3 {(0)}^{2}}{2 {(0)}^{2} - 32}$

Step 3.2

Solve the equation.

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Step 3.2.1

Remove parentheses.

$y = \frac{3 \cdot 0^{2}}{2 {(0)}^{2} - 32}$

Step 3.2.2

Remove parentheses.

$y = \frac{3 \cdot 0^{2}}{2 \cdot 0^{2} - 32}$

Step 3.2.3

Remove parentheses.

$y = \frac{3 {(0)}^{2}}{2 {(0)}^{2} - 32}$

Step 3.2.4

Simplify $\frac{3 {(0)}^{2}}{2 {(0)}^{2} - 32}$ .

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Step 3.2.4.1

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

$y = \frac{3 \cdot 0}{2 \cdot 0^{2} - 32}$

Step 3.2.4.2

Simplify the denominator.

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Step 3.2.4.2.1

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

$y = \frac{3 \cdot 0}{2 \cdot 0 - 32}$

Step 3.2.4.2.2

Multiply $2$ by $0$ .

$y = \frac{3 \cdot 0}{0 - 32}$

Step 3.2.4.2.3

Subtract $32$ from $0$ .

$y = \frac{3 \cdot 0}{- 32}$

Step 3.2.4.3

Simplify the expression.

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Step 3.2.4.3.1

Multiply $3$ by $0$ .

$y = \frac{0}{- 32}$

Step 3.2.4.3.2

Divide $0$ by $- 32$ .

$y = 0$

Step 3.3

y-intercept(s) in point form.

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

Step 4

List the intersections.

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

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

Step 5