Find the Domain 1/(x/(x+1))

$\frac{1}{\frac{x}{x + 1}}$

Step 1

Set the denominator in $\frac{x}{x + 1}$ equal to $0$ to find where the expression is undefined.

$x + 1 = 0$

Step 2

Subtract $1$ from both sides of the equation.

$x = - 1$

Step 3

Set the denominator in $\frac{1}{\frac{x}{x + 1}}$ equal to $0$ to find where the expression is undefined.

$\frac{x}{x + 1} = 0$

Step 4

Set the numerator equal to zero.

$x = 0$

Step 5

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

Interval Notation:

$(- \infty, - 1) \cup (- 1, 0) \cup (0, \infty)$

Set-Builder Notation:

${x | x \neq 0, - 1}$

Step 6