SOLUTION: (a^negative 1 - b^ negative 1)^ negative 1 I keep doing this, and getting a-b. I have the answer (its in the back of the book) ab/b-a , but I don't know how they got it.

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: (a^negative 1 - b^ negative 1)^ negative 1 I keep doing this, and getting a-b. I have the answer (its in the back of the book) ab/b-a , but I don't know how they got it.      Log On


   

Question 131558: (a^negative 1 - b^ negative 1)^ negative 1
I keep doing this, and getting a-b.
I have the answer (its in the back of the book) ab/b-a , but I don't know how they got it.
Found 2 solutions by josmiceli, solver91311:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
%28a%5E%28-1%29+-+b%5E%28-1%29%29%5E%28-1%29
note that a%5E%28-1%29+=+1%2Fa ,and also b%5E%28-1%29+=+1%2Fb
%28%281%2Fa%29+-+%281%2Fb%29%29%5E%28-1%29
and, likewise,
%28%281%2Fa%29+-+%281%2Fb%29%29%5E%28-1%29+=+1+%2F+%28%281%2Fa%29+-+%281%2Fb%29%29
Now multiply the top and bottom by ab
ab+%2F+%28b+-+a%29 answer

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E%28-1%29=1%2Fx for all real numbers x, x%3C%3E0.

So, %28a%5E%28-1%29-b%5E%28-1%29%29%5E-1=1%2F%281%2Fa-1%2Fb%29

In order to add the two fractions in the denominator, you need a lowest common denominator. Without any factors in common that we know about, the best we can do for a common denominator is ab, so:



Note that the original expression is undefined if either a=0, b=0, OR a=b, but the only restriction on the final expression is that a%3C%3Eb