Given:
There are given that the expression:
[tex]\frac{\sqrt{x+5}}{\sqrt{1-x}}[/tex]
Explanation;
First, let's notice that we need positives to numbers inside both roots.
So,
The root of a negative number is a math error.
Then,
With that information, let us analyze the options.
From option A:
If we add 5 to this inequality, we have:
[tex]\begin{gathered} -5+5\leq x+5<1+5 \\ 0\leq x+5<6 \end{gathered}[/tex]
That means the number in the first root is positive.
Now, we want 1-x to be positive:
[tex]\begin{gathered} -5\leq x<1 \\ 5\ge-x>-1 \\ 1+5\ge1-x>1-1 \\ 6\ge1-x>0 \end{gathered}[/tex]
So, it is positive:
Final answer;
Hence, the correct option is A.
