Find the domain of the function $f(x)=\frac{1}{2 x+5}$. What is the only value of $x$ not in the domain?
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Step 1 ：The domain of a function is the set of all possible input values (often denoted as x) that will output a real number. In this case, the function is a rational function, and the denominator cannot be zero because division by zero is undefined in mathematics. Therefore, we need to find the value of x that makes the denominator zero, and this value will not be in the domain of the function.

Step 2 ：Let's find the value of x that makes the denominator zero. We set the denominator equal to zero and solve for x: \(2x + 5 = 0\)

Step 3 ：The solution to the equation \(2x + 5 = 0\) is \(x = -\frac{5}{2}\). This is the value of x that makes the denominator of the function zero, and therefore it is the only value not in the domain of the function.

Step 4 ：Final Answer: The only value of \(x\) not in the domain of the function \(f(x)=\frac{1}{2 x+5}\) is \(\boxed{-\frac{5}{2}}\).