SOLUTION: ((x^2(1+x^2)^(1/2))-(x^2(1+x^2)^(-1/2)))/(1+x^2) What is the domain of the question above? and also would you be kind enough to show me the steps?

Algebra ->  Functions -> SOLUTION: ((x^2(1+x^2)^(1/2))-(x^2(1+x^2)^(-1/2)))/(1+x^2) What is the domain of the question above? and also would you be kind enough to show me the steps?      Log On


   

Question 650759: ((x^2(1+x^2)^(1/2))-(x^2(1+x^2)^(-1/2)))/(1+x^2)
What is the domain of the question above? and also would you be kind enough to show me the steps?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

To find the domain, I'll ignore the "" in the numerator (since the numerator does not
cause division by zero) and instead I'll look at the denominator
1%2Bx%5E2.
I'll set the denominator equal to zero, and solve.
1%2Bx%5E2=0
The x-values in the solution will be the x-values which would cause
division by zero. The domain will then be all other x-values.
x%5E2=-1
x=sqrt%28-1%29
x=i and x=-i

...as you can see here, whatever x is, the denominator will NOT be equal
to zero
so, the domain will be all real numbers from -infinity to infinity

(-infinity ,infinity)