Precalculus Examples

$\sqrt{x - 3} + \sqrt{x + 1} = \frac{3}{5 - x}$

Step 1

Set the radicand in $\sqrt{x - 3}$ greater than or equal to $0$ to find where the expression is defined.

$x - 3 \geq 0$

Step 2

Add $3$ to both sides of the inequality.

$x \geq 3$

Step 3

Set the radicand in $\sqrt{x + 1}$ greater than or equal to $0$ to find where the expression is defined.

$x + 1 \geq 0$

Step 4

Subtract $1$ from both sides of the inequality.

$x \geq - 1$

Step 5

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

Interval Notation:

$[3, \infty)$

Set-Builder Notation:

${x | x \geq 3}$

Step 6