domain of (sqrt(x+1))/(sqrt(x)) — step-by-step solution

Let's find the domain of

\frac{\sqrt{x + 1}}{\sqrt{x}}

For the expression

\sqrt{x + 1}

to be defined, we must have:

x + 1 \geq 0

For the expression

\frac{\sqrt{x + 1}}{\sqrt{x}}

to be defined, we must have:

x > 0

Let's solve in

ℝ

x + 1 \geq 0

ⓘ We subtract

1

from both sides

Solution found:

x \geq -1

Intersecting

x \geq -1

and

x > 0

gives

x > 0

▶Domain of definition:

x > 0