[(1-x^2)^1/2+x^2(1-x^2)^-1/2]/1-x^2

Question

Simplify the expression

Answer 1

Hi Vianna,

 

Ok let's cleanup the problem a bit first:

 

( √(1-x²) + x²/√(1-x²) ) / (1-x²)

 

Sorry, it is just a little easier to read that way I find. Ok, so let's work with the numerator first:

 

√(1-x²) + x²/√(1-x²)

 

We want to write this as one fraction, so let's do that:

 

√(1-x²)*( √(1-x²)/√(1-x²) ) + x²/√(1-x²) = (1-x²)/√(1-x²) + x²/√(1-x²)

 

                                                             = (1-x²+x²)/√(1-x²)

 

                                                             =1/√(1-x²)

 

Ok so this is the numerator, and substituting this back into our equation gives us

 

( 1/√(1-x²) )/(1-x²) = 1/( (1-x²)√(1-x²) )

 

                              = 1/x^3/2

 

                              = x^-3/2