Finite Math Examples

$\frac{\sqrt{3 x^{4} + 4}}{9 x^{4} - 4 x^{3}}$

Step 1

Set the denominator in $\frac{\sqrt{3 x^{4} + 4}}{9 x^{4} - 4 x^{3}}$ equal to $0$ to find where the expression is undefined.

$9 x^{4} - 4 x^{3} = 0$

Step 2

Solve for $x$ .

Tap for more steps...

Step 2.1

Factor $x^{3}$ out of $9 x^{4} - 4 x^{3}$ .

Tap for more steps...

Step 2.1.1

Factor $x^{3}$ out of $9 x^{4}$ .

$x^{3} (9 x) - 4 x^{3} = 0$

Step 2.1.2

Factor $x^{3}$ out of $- 4 x^{3}$ .

$x^{3} (9 x) + x^{3} \cdot - 4 = 0$

Step 2.1.3

Factor $x^{3}$ out of $x^{3} (9 x) + x^{3} \cdot - 4$ .

$x^{3} (9 x - 4) = 0$

Step 2.2

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

$x^{3} = 0$

$9 x - 4 = 0$

Step 2.3

Set $x^{3}$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 2.3.1

Set $x^{3}$ equal to $0$ .

$x^{3} = 0$

Step 2.3.2

Solve $x^{3} = 0$ for $x$ .

Tap for more steps...

Step 2.3.2.1

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

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

Step 2.3.2.2

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

Tap for more steps...

Step 2.3.2.2.1

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

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

Step 2.3.2.2.2

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

$x = 0$

Step 2.4

Set $9 x - 4$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 2.4.1

Set $9 x - 4$ equal to $0$ .

$9 x - 4 = 0$

Step 2.4.2

Solve $9 x - 4 = 0$ for $x$ .

Tap for more steps...

Step 2.4.2.1

Add $4$ to both sides of the equation.

$9 x = 4$

Step 2.4.2.2

Divide each term in $9 x = 4$ by $9$ and simplify.

Tap for more steps...

Step 2.4.2.2.1

Divide each term in $9 x = 4$ by $9$ .

$\frac{9 x}{9} = \frac{4}{9}$

Step 2.4.2.2.2

Simplify the left side.

Tap for more steps...

Step 2.4.2.2.2.1

Cancel the common factor of $9$ .

Tap for more steps...

Step 2.4.2.2.2.1.1

Cancel the common factor.

$\frac{9 x}{9} = \frac{4}{9}$

Step 2.4.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{4}{9}$

Step 2.5

The final solution is all the values that make $x^{3} (9 x - 4) = 0$ true.

$x = 0, \frac{4}{9}$

Step 3

Set the radicand in $\sqrt{3 x^{4} + 4}$ less than $0$ to find where the expression is undefined.

$3 x^{4} + 4 < 0$

Step 4

Solve for $x$ .

Tap for more steps...

Step 4.1

Subtract $4$ from both sides of the inequality.

$3 x^{4} < - 4$

Step 4.2

Divide each term in $3 x^{4} < - 4$ by $3$ and simplify.

Tap for more steps...

Step 4.2.1

Divide each term in $3 x^{4} < - 4$ by $3$ .

$\frac{3 x^{4}}{3} < \frac{- 4}{3}$

Step 4.2.2

Simplify the left side.

Tap for more steps...

Step 4.2.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 4.2.2.1.1

Cancel the common factor.

$\frac{3 x^{4}}{3} < \frac{- 4}{3}$

Step 4.2.2.1.2

Divide $x^{4}$ by $1$ .

$x^{4} < \frac{- 4}{3}$

Step 4.2.3

Simplify the right side.

Tap for more steps...

Step 4.2.3.1

Move the negative in front of the fraction.

$x^{4} < - \frac{4}{3}$

Step 4.3

Since the left side has an even power, it is always positive for all real numbers.

No solution

Step 5

The equation is undefined where the denominator equals $0$ , the argument of a square root is less than $0$ , or the argument of a logarithm is less than or equal to $0$ .

$x = 0, x = \frac{4}{9}$

Step 6