Finding the Domain of (2x+2)/√(x+2.5): Rational Function Analysis

To find the domain of the function $\frac{2x+2}{\sqrt{x+2.5}}$, we need to determine for which values of $x$ the expression is defined.

Step 1: Identify the restriction on the square root.
The square root function $\sqrt{x+2.5}$ is defined when the expression inside the square root is non-negative. Thus, we have the inequality:

$x + 2.5 \geq 0$

Step 2: Solve the inequality for $x$.
Subtract 2.5 from both sides:

$x \geq -2.5$

Step 3: Ensure the denominator is not zero because division by zero is undefined.
Since $x + 2.5 \neq 0$, we require:

$x \neq -2.5$

Therefore, combining these results, the domain of the function is:

$x > -2.5$

The correct answer to the problem, represented as a choice, is:

x > -2.5