Set the radicand in <math><mstyle displaystyle="true"><msqrt><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></msqrt></mstyle></math> greater than or equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> to find where the expression is defined.

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

All real numbers

Set the denominator in <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><msqrt><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></msqrt><mo>-</mo><mn>4</mn></mrow></mfrac></mstyle></math> equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> to find where the expression is undefined.

Add <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> to both sides of the equation.

To remove the radical on the left side of the equation, square both sides of the equation.

Simplify each side of the equation.

Multiply the exponents in <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><msup><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Apply the power rule and multiply exponents, <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msup><mo>)</mo></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi><mi>n</mi></mrow></msup></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Solve for <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

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

The complete solution is the result of both the positive and negative portions of the solution.

Simplify the right side of the equation.

Rewrite <math><mstyle displaystyle="true"><mn>16</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>4</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

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

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the <math><mstyle displaystyle="true"><mo>±</mo></mstyle></math> to find the first solution.

Next, use the negative value of the <math><mstyle displaystyle="true"><mo>±</mo></mstyle></math> to find the second solution.

The complete solution is the result of both the positive and negative portions of the solution.

The domain is all values of <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> that make the expression defined.

Interval Notation:

Set-Builder Notation:

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