Find the smallest integer x where the expression sqrt (x+8)/(x^2+x+16) is defined.

Guest Oct 25, 2022

#1**0 **

The expression \(\dfrac{\sqrt{x+8}}{x^2+x+16}\) is defined if:

\(x+8\ge 0 \implies x\ge -8\)

AND

\(x^2+x+16 \neq 0 \\ \text{Which, in real numbers, is already satisified; as it only equals 0 if x is a complex number.}\)

So the smallest x for which this expression is defined is -8.

Guest Oct 25, 2022