sqrt(x/(x-1)) = sqrt(x)/sqrt(x-1)?

All right, so it's kind of obvious that they are equal for x >= 0 (the latter may be different because of the domain of sqrt), but is it true that they are always equal?

Using x = -4 as an example:
sqrt(-4/-5) = 2*sqrt(5)/5
sqrt(-4)/sqrt(-5) = (2i)/(sqrt(5)*i) = 2*sqrt(5)/5

You are a true nigger.

x = 1/2

Ah, I didn't even think to look on 0 < x < 1, but I suppose I should have. Thanks.

In complex field it is valid that sqrt(ab)=sqrt(a)sqrt(b) if and only if -π<arg(a) + arg(b)<=π

That property is always true when both roots are of non-negative numbers. When one or both of them get you complex answers, it's not always true. In fact, misusing that property is one of the more popular ways to "prove" that 2 = 1.

sqrt(a/b)=(a/b)^(1/2)=[a*(b^-1)]^1/2=(a^1/2)*(b^-1/2)=sqrt(a)/sqrt(b)
Laws of indicies, learn them

>[a*(b^-1)]^1/2=(a^1/2)*(b^-1/2)
lol phail

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