To find the value of x, we have to know:
- The denominator can not be zero
- The radical must be zero or greater than zero
So, let's evaluate the numerator and the denominator
a)
[tex]x+2\ge0[/tex]Subtracting 2 from both sides:
[tex]\begin{gathered} x+2-2\ge0-2 \\ x\ge-2 \end{gathered}[/tex]b)
[tex]5-x>0[/tex]Adding x to both sides:
[tex]\begin{gathered} 5-x+x>0+x \\ 5>x \\ x<5 \end{gathered}[/tex]So, x must b greater or equal to 2 and lower than 5.
Answer:
[tex]2\leq x<5[/tex]