In the denominator, it's clear that x 2 goes to 1 as x approaches 1 . So the difference inside the square root function must go zero.
Square root is a continuous function for nonnegative x , and the square root of zero is zero.
So this limit qualifies for L'Hopital's rule. Take the derivatives of the numerator and denominator. Apply L'Hopital's Rule. You can experiment on your calculator with taking the original function of x 's that are very close to 1 to confirm this limit.