document.write( "Question 206640: I need to simplify x^-1+2/x+2x^2 \r
\n" ); document.write( "\n" ); document.write( "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. \n" ); document.write( "
Algebra.Com's Answer #156169 by ichudov(507)\"\" \"About 
You can put this solution on YOUR website!
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Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:

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  • 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 )
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  • If you have a website, here's a link to this solution.
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DETAILED EXPLANATION

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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\".
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Look at \"1%2Fx%5Ehighlight_red%28+1+%29%2B2%2Fx%2B2%2Ax%5E2\".
Removing power of one \"highlight_red%28+1+%29\"
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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\".
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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\".
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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\"
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Universal Simplifier and Solver

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Done!
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