SOLUTION: Good morning guys here is my question simplify: x^-1+2x^-2 __________ 1+x^-1 what i have done so far is change the symbols to positives. x^1+2x^2 ________ 1+

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Good morning guys here is my question simplify: x^-1+2x^-2 __________ 1+x^-1 what i have done so far is change the symbols to positives. x^1+2x^2 ________ 1+      Log On


   

Question 277509: Good morning guys
here is my question
simplify:
x^-1+2x^-2
__________
1+x^-1
what i have done so far is change the symbols to positives.
x^1+2x^2
________
1+x^1
after this i get lost.
the most plausible answer seems to be
x+2
___
x(x+1)
any help is appreciated. Thank you!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%5E%28-1%29%2B2x%5E%28-2%29%29%2F%281%2Bx%5E%28-1%29%29 Start with the given expression.


%281%2Fx%2B2%2F%28x%5E2%29%29%2F%281%2B1%2Fx%29 Rewrite sub expression with positive exponents (just flip the base)


Multiply EVERY term by the inner LCD x%5E2 to clear out the inner fractions.


%28x%2B2%29%2F%28x%5E2%2Bx%29 Simplify


So %28x%5E%28-1%29%2B2x%5E%28-2%29%29%2F%281%2Bx%5E%28-1%29%29=%28x%2B2%29%2F%28x%5E2%2Bx%29 which is equivalent to what you have (you just have the denominator factored)