Trigonometry Examples

$\frac{x^{2}}{x - 4} = \frac{16}{x - 4}$

Step 1

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$x^{2} = 16$

Step 2

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

$x = \pm \sqrt{16}$

Step 3

Simplify $\pm \sqrt{16}$ .

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Step 3.1

Rewrite $16$ as $4^{2}$ .

$x = \pm \sqrt{4^{2}}$

Step 3.2

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

$x = \pm 4$

Step 4

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

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Step 4.1

First, use the positive value of the $\pm$ to find the first solution.

$x = 4$

Step 4.2

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 4$

Step 4.3

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

$x = 4, - 4$

Step 5

Exclude the solutions that do not make $\frac{x^{2}}{x - 4} = \frac{16}{x - 4}$ true.

$x = - 4$