Precalculus Examples

$\frac{x^{2} + x^{3}}{11 a^{2}} \div \frac{4 + 4 x}{a^{3}}$

Step 1

Set the denominator in $\frac{x^{2} + x^{3}}{11 a^{2}}$ equal to $0$ to find where the expression is undefined.

$11 a^{2} = 0$

Step 2

Solve for $x$ .

Tap for more steps...

Step 2.1

Divide each term in $11 a^{2} = 0$ by $11$ and simplify.

Tap for more steps...

Step 2.1.1

Divide each term in $11 a^{2} = 0$ by $11$ .

$\frac{11 a^{2}}{11} = \frac{0}{11}$

Step 2.1.2

Simplify the left side.

Tap for more steps...

Step 2.1.2.1

Cancel the common factor of $11$ .

Tap for more steps...

Step 2.1.2.1.1

Cancel the common factor.

$\frac{11 a^{2}}{11} = \frac{0}{11}$

Step 2.1.2.1.2

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

$a^{2} = \frac{0}{11}$

Step 2.1.3

Simplify the right side.

Tap for more steps...

Step 2.1.3.1

Divide $0$ by $11$ .

$a^{2} = 0$

Step 2.2

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

$a = \pm \sqrt{0}$

Step 2.3

Simplify $\pm \sqrt{0}$ .

Tap for more steps...

Step 2.3.1

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

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

Step 2.3.2

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

$a = \pm 0$

Step 2.3.3

Plus or minus $0$ is $0$ .

$a = 0$

Step 3

Set the denominator in $\frac{4 + 4 x}{a^{3}}$ equal to $0$ to find where the expression is undefined.

$a^{3} = 0$

Step 4

Solve for $x$ .

Tap for more steps...

Step 4.1

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

$a = \sqrt[3]{0}$

Step 4.2

Simplify $\sqrt[3]{0}$ .

Tap for more steps...

Step 4.2.1

Rewrite $0$ as $0^{3}$ .

$a = \sqrt[3]{0^{3}}$

Step 4.2.2

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

$a = 0$

Step 5

Set the denominator in $\frac{x^{2} + x^{3}}{11 a^{2}} \div \frac{4 + 4 x}{a^{3}}$ equal to $0$ to find where the expression is undefined.

$\frac{4 + 4 x}{a^{3}} = 0$

Step 6

Solve for $x$ .

Tap for more steps...

Step 6.1

Set the numerator equal to zero.

$4 + 4 x = 0$

Step 6.2

Solve the equation for $x$ .

Tap for more steps...

Step 6.2.1

Subtract $4$ from both sides of the equation.

$4 x = - 4$

Step 6.2.2

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

Tap for more steps...

Step 6.2.2.1

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

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

Step 6.2.2.2

Simplify the left side.

Tap for more steps...

Step 6.2.2.2.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 6.2.2.2.1.1

Cancel the common factor.

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

Step 6.2.2.2.1.2

Divide $x$ by $1$ .

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

Step 6.2.2.3

Simplify the right side.

Tap for more steps...

Step 6.2.2.3.1

Divide $- 4$ by $4$ .

$x = - 1$

Step 7

The domain is all values of $x$ that make the expression defined.

Interval Notation:

$(- \infty, - 1) \cup (- 1, 0) \cup (0, \infty)$

Set-Builder Notation:

${x | x \neq 0, - 1}$