Trigonometry Examples

$\frac{x^{2} - 1}{x - 3} = \frac{8}{x - 3}$

Step 1

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

$x^{2} - 1 = 8$

Step 2

Move all terms not containing $x$ to the right side of the equation.

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Step 2.1

Add $1$ to both sides of the equation.

$x^{2} = 8 + 1$

Step 2.2

Add $8$ and $1$ .

$x^{2} = 9$

Step 3

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

$x = \pm \sqrt{9}$

Step 4

Simplify $\pm \sqrt{9}$ .

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Step 4.1

Rewrite $9$ as $3^{2}$ .

$x = \pm \sqrt{3^{2}}$

Step 4.2

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

$x = \pm 3$

Step 5

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

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Step 5.1

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

$x = 3$

Step 5.2

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

$x = - 3$

Step 5.3

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

$x = 3, - 3$

Step 6

Exclude the solutions that do not make $\frac{x^{2} - 1}{x - 3} = \frac{8}{x - 3}$ true.

$x = - 3$