Algebra Examples

\frac{1}{(\frac{1}{x})}

$\frac{1}{(\frac{1}{x})}$

Step 1

Set the denominator in

\frac{1}{x}

$\frac{1}{x}$ equal to

0

$0$ to find where the expression is undefined.

x = 0

$x = 0$

Step 2

Set the denominator in

\frac{1}{\frac{1}{x}}

$\frac{1}{\frac{1}{x}}$ equal to

0

$0$ to find where the expression is undefined.

\frac{1}{x} = 0

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

Step 3

Solve for

x

$x$ .

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Step 3.1

Set the numerator equal to zero.

1 = 0

$1 = 0$

Step 3.2

Since

1 \neq 0

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

No solution

No solution

Step 4

The domain is all values of

x

$x$ that make the expression defined.

Interval Notation:

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

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

Set-Builder Notation:

{x | x \neq 0}

${x | x \neq 0}$

Step 5

⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$