SOLUTION: x^-1 + y^-1/x^-1 simplify write the answers with all exponents positive

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: x^-1 + y^-1/x^-1 simplify write the answers with all exponents positive       Log On


   

Question 66958This question is from textbook Algebra 1
: x^-1 + y^-1/x^-1

simplify write the answers with all exponents positive This question is from textbook Algebra 1

Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
+%28x%5E%28-1%29+%2B+y%5E%28-1%29%29%2Fx%5E%28-1%29+

simplify write the answers with all exponents positive 

You didn't put any parentheses to show where numerator
and denominator begin and end, so I can't tell whether 
you mean

+%28x%5E%28-1%29+%2B+y%5E%28-1%29%29%2Fx%5E%28-1%29+

or whether you mean

x%5E%28-1%29+%2B+y%5E%28-1%29%2Fx%5E%28-1%29
 
-----------------------------------

If it's the first way

+%28x%5E%28-1%29+%2B+y%5E%28-1%29%29%2Fx%5E%28-1%29+

Use the rule: A%5E%28-n%29=1%2FA%5E%28n%29 to rewrite
all the terms in numerator and denominator

+%281%2Fx%5E%281%29+%2B+1%2Fy%5E%281%29%29%2F%281%2Fx%5E%281%29%29

Now we can erase all the 1 exponents:

+%281%2Fx+%2B+1%2Fy%29%2F%281%2Fx%29

Now look at all the denominators in the main
numerator and the main denominator.  They are
x, y and y.  The LCD is then xy, so we multiply
by %28xy%29%2F%28xy%29 but write it as%28%28xy%29%2F1%29%2F%28%28xy%29%2F1%29%29

%28%28xy%29%2F1%29%2F%28%28xy%29%2F1%29%29·+%28%281%2Fx+%2B+1%2Fy%29%29%2F%281%2Fx%29

Now distribute the %28xy%29%2F1%29 in the numerator
and indicate the multiplication of the denominators



Cancel the x's in the first term on top, and just get y
Cancel the y's in the second term on top, and just get x
and cancel the x's in the term on the bottom, and just get y

So the answer is just

%28y+%2B+x%29%2Fy

Edwin