The path to simplifying this expression shown by the other tutor is a perfectly sound mathematical process. It is the one that would very likely be used by a student who is first learning about fractional and negative exponents.
There is a different approach that gets you to the final answer shown by the other tutor in a single step.
Given "a+a^-1" in the denominator of the expression, multiply numerator and denominator of the expression by a to get rid of the negative exponent:
