Question 888276
{{{sqrt(x^2 - 1) / sqrt(x-1)}}} = {{{sqrt((x^2-1)/(x-1))}}} = {{{sqrt((x-1)(x+1)/(x-1))}}} = {{{sqrt(x+1)}}}


following is the graph of the equation of {{{sqrt(x^2 - 1) / sqrt(x-1)}}}


<img src = "http://theo.x10hosting.com/2014/072001.jpg" alt="$$$" </>


following is the graph of the equation of {{{sqrt(x+1)}}}


<img src = "http://theo.x10hosting.com/2014/072002.jpg" alt="$$$" </>


the first graph doesn't allow values of x = 1 because that would make the denominator equal to 0 and the function would be undefined.


the first graph also doesn't allow values of x <1 because that would make the numerator the squart root of a negative number which is also undefined in the real number system.


the second graph goes to 0 because x+1 will be positive for values less than 1 of x but greater than or equal to 0 and will also allows x = 1 because there is no denominator in that equation.


the 2 equations are equivalent except that once you eliminated the denominator by canceling it out, you can then get a defined solution at x = 1.