Calculus Examples

$\frac{x^{2} + 14 x + 1}{{(x + 1)}^{2}}$

Step 1

Set the denominator in $\frac{x^{2} + 14 x + 1}{{(x + 1)}^{2}}$ equal to $0$ to find where the expression is undefined.

${(x + 1)}^{2} = 0$

Step 2

Solve for $x$ .

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Step 2.1

Set the $x + 1$ equal to $0$ .

$x + 1 = 0$

Step 2.2

Subtract $1$ from both sides of the equation.

$x = - 1$

Step 3

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

Interval Notation:

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

Set-Builder Notation:

${x | x \neq - 1}$

Step 4