Precalculus Examples

$\frac{\frac{8}{x}}{\frac{10}{x + 10}}$

Step 1

Set the denominator in $\frac{8}{x}$ equal to $0$ to find where the expression is undefined.

$x = 0$

Step 2

Set the denominator in $\frac{10}{x + 10}$ equal to $0$ to find where the expression is undefined.

$x + 10 = 0$

Step 3

Subtract $10$ from both sides of the equation.

$x = - 10$

Step 4

Set the denominator in $\frac{\frac{8}{x}}{\frac{10}{x + 10}}$ equal to $0$ to find where the expression is undefined.

$\frac{10}{x + 10} = 0$

Step 5

Solve for $x$ .

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Step 5.1

Set the numerator equal to zero.

$10 = 0$

Step 5.2

Since $10 \neq 0$ , there are no solutions.

No solution

Step 6

The domain is all values of $x$ that make the expression defined.

Interval Notation:

$(- \infty, - 10) \cup (- 10, 0) \cup (0, \infty)$

Set-Builder Notation:

${x | x \neq 0, - 10}$

Step 7