SOLUTION: I need to simplify x^-1+2/x+2x^2 I know that x^-1 is equal to 1/x. I get a little confused on what to do next. Do I add or multiply the 1/x to what is left--which would be 2/x+

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I need to simplify x^-1+2/x+2x^2 I know that x^-1 is equal to 1/x. I get a little confused on what to do next. Do I add or multiply the 1/x to what is left--which would be 2/x+      Log On


   

Question 206640: I need to simplify x^-1+2/x+2x^2
I know that x^-1 is equal to 1/x. I get a little confused on what to do next. Do I add or multiply the 1/x to what is left--which would be 2/x+2x^2. Any help you can provide would be greatly appreciated.
Found 2 solutions by ichudov, MathTherapy:
Answer by ichudov(507) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Graphical form: x%5E%28-1%29%2B2%2Fx%2B2x%5E2 simplifies to 3%2Fx%2B2%2Ax%5E2
  • Text form: x^(-1)+2/x+2x^2 simplifies to 3/x+2*x^2
  • Cartoon (animation) form: simplify_cartoon%28+x%5E%28-1%29%2B2%2Fx%2B2x%5E2+%29
    For tutors: simplify_cartoon( x^(-1)+2/x+2x^2 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+x%5E%28-1%29+%29%2B2%2Fx%2B2%2Ax%5E2.
Negative power changes multiplication to division
It becomes 1%2Fhighlight_green%28+x%5E1+%29%2B2%2Fx%2B2%2Ax%5E2.
Look at 1%2Fx%5Ehighlight_red%28+1+%29%2B2%2Fx%2B2%2Ax%5E2.
Removing power of one highlight_red%28+1+%29
Look at highlight_red%28+1%2Fx+%29%2Bhighlight_red%28+2%2Fx+%29%2B2%2Ax%5E2.
Eliminated similar terms highlight_red%28+1%2Fx+%29,highlight_red%28+2%2Fx+%29 replacing them with highlight_green%28+%281%2B2%29%2Fx+%29
It becomes highlight_green%28+%281%2B2%29%2Fx+%29%2B2%2Ax%5E2.
Look at %28highlight_red%28+1+%29%2Bhighlight_red%28+2+%29%29%2Fx%2B2%2Ax%5E2.
Added fractions or integers together
It becomes %28highlight_green%28+3+%29%29%2Fx%2B2%2Ax%5E2.
Look at highlight_red%28+%28highlight_red%28+3+%29%29%2Fx+%29%2B2%2Ax%5E2.
Remove unneeded parentheses around factor highlight_red%28+3+%29
It becomes highlight_green%28+3+%29%2Fx%2B2%2Ax%5E2.
Result: 3%2Fx%2B2%2Ax%5E2

Universal Simplifier and Solver


Done!

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

simplify x%5E%28-1%29%2B2%2Fx%2B2x%5E2

x%5E%28-1%29%2B2%2Fx%2B2x%5E2 ------> 1%2Fx%5E1%2B2%2Fx%2B2x%5E2 ------> %281%2B2%2B2x%5E3%29%2Fx------> %283%2B2x%5E3%29%2Fx ------> highlight_green%283%2Fx%2B2x%5E2%29