Trigonometry Examples

$\frac{\sqrt{3 x - 16} - 5}{x - 3}$

Step 1

Set the denominator in $\frac{\sqrt{3 x - 16} - 5}{x - 3}$ equal to $0$ to find where the expression is undefined.

$x - 3 = 0$

Step 2

Add $3$ to both sides of the equation.

$x = 3$

Step 3

Set the radicand in $\sqrt{3 x - 16}$ less than $0$ to find where the expression is undefined.

$3 x - 16 < 0$

Step 4

Solve for $x$ .

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Step 4.1

Add $16$ to both sides of the inequality.

$3 x < 16$

Step 4.2

Divide each term in $3 x < 16$ by $3$ and simplify.

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Step 4.2.1

Divide each term in $3 x < 16$ by $3$ .

$\frac{3 x}{3} < \frac{16}{3}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $3$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} < \frac{16}{3}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x < \frac{16}{3}$

Step 5

The equation is undefined where the denominator equals $0$ , the argument of a square root is less than $0$ , or the argument of a logarithm is less than or equal to $0$ .

$x < \frac{16}{3}$

$(- \infty, \frac{16}{3})$

Step 6