domain of (sqrt(x+8)+2)/(x+2) — step-by-step solution

1) Let's find the domain of

\frac{\sqrt{x + 8} + 2}{x + 2}

For the expression

\frac{\sqrt{x + 8} + 2}{x + 2}

to exist, you must check:

x + 2 \neq 0

For the expression

\sqrt{x + 8}

to be defined, we must have:

x + 8 \geq 0

2) Let's solve in

ℝ

x + 2 \neq 0

ⓘ We subtract

2

from both sides

Solution found:

x \neq -2

3) Let's solve in

ℝ

x + 8 \geq 0

ⓘ We subtract

8

from both sides

Solution found:

x \geq -8

Let's build the table of the different terms to determine the global solution:

▶Domain of definition:

x \in [-8, -2) \cup (-2, +∞)