How do you expand (x+h)^-1

Question

How do you expand (x+h)^-1. I'm trying to find the limit definition of x^2+x^-1. Essentially (f(x+h)-f(x))/h. I know how to expand x^2. I just don't know how to expand x^-1.

Thank you so much!

Answer 1

It's the reciprocal of the quantity in parentheses, i.e.  1/(x+h).  x^-1 is 1/x.

 

To do this work, you'll be using the common denominator of the difference that is in the numerator, during the algebra work.  Replace the overall division by h by making 1/h a factor!