Question 650759
{{{((x^2(1+x^2)^(1/2))-(x^2(1+x^2)^(-1/2)))/(1+x^2)}}}

To find the domain, I'll ignore the "{{{((x^2(1+x^2)^(1/2))-(x^2(1+x^2)^(-1

/2)))}}}" in the numerator (since the numerator {{{does}}} {{{not}}} 

cause division by {{{zero}}}) and instead I'll look at the {{{denominator}}} 

{{{1+x^2}}}. 

I'll set the denominator equal to {{{zero}}}, and solve. 

{{{1+x^2=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^2=-1}}}

{{{x=sqrt(-1)}}}

{{{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}}})