Finite Math Examples

\frac{x^{2 - 4}}{x} > 0

$\frac{x^{2 - 4}}{x} > 0$

Step 1

Find all the values where the expression switches from negative to positive by setting each factor equal to

0

$0$ and solving.

x^{2 - 4} = 0

$x^{2 - 4} = 0$

x = 0

$x = 0$

Step 2

Simplify

x^{2 - 4}

$x^{2 - 4}$ .

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Step 2.1

Subtract

4

$4$ from

2

$2$ .

x^{- 2} = 0

$x^{- 2} = 0$

Step 2.2

Rewrite the expression using the negative exponent rule

b^{- n} = \frac{1}{b^{n}}

$b^{- n} = \frac{1}{b^{n}}$ .

\frac{1}{x^{2}} = 0

$\frac{1}{x^{2}} = 0$

\frac{1}{x^{2}} = 0

$\frac{1}{x^{2}} = 0$

Step 3

Set the numerator equal to zero.

1 = 0

$1 = 0$

Step 4

Since

1 \neq 0

$1 \neq 0$ , there are no solutions.

No solution

Step 5

Solve for each factor to find the values where the absolute value expression goes from negative to positive.

x = 0

$x = 0$

Step 6

The domain is all values of

x

$x$ that make the expression defined.

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

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

Step 7

The solution consists of all of the true intervals.

x > 0

$x > 0$

Step 8

The result can be shown in multiple forms.

Inequality Form:

x > 0

$x > 0$

Interval Notation:

(0, \infty)

$(0, \infty)$

Step 9