sqrt(4-x^2) divided by sqrt (1-x^2)

Question

Botth radicands  must be non-negative, and can't be divided by zero.

Answer 1

√(4-x²)/√(1-x²) is the same as √((4-x²)/(1-x²)).

The radicand can also be written:

(x²-4)/(x²-1)=((x²-1)-3)/(x²-1)=1-3/(x²-1)=1+3/(1-x²).

So the quotient is √(1+3/(1-x²)) for x²<1, that is, -1<x<1.