Trigonometry Examples

$\frac{30}{x^{2} - 9} + 1 = \frac{5}{x - 3}$

Step 1

Simplify the denominator.

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Step 1.1

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

$\frac{30}{x^{2} - 3^{2}} + 1 = \frac{5}{x - 3}$

Step 1.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 3$ .

$\frac{30}{(x + 3) (x - 3)} + 1 = \frac{5}{x - 3}$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x = 2$

Step 3