SOLUTION: Add or Subtract y^3 - 5y/6y - y^3 + y + 3/6y

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Question 173756: Add or Subtract
y^3 - 5y/6y - y^3 + y + 3/6y
Answer by jojo14344(1513) 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: y%5E3-%285y%2F6%2Fy%29-y%5E3%2By%2B%283%2F6%2Fy%29 simplifies to y%2B1%2F2%2Fy-5%2F6
  • Text form: y^3-(5y/6/y)-y^3+y+(3/6/y) simplifies to y+1/2/y-5/6
  • Cartoon (animation) form: simplify_cartoon%28+y%5E3-%285y%2F6%2Fy%29-y%5E3%2By%2B%283%2F6%2Fy%29+%29
    For tutors: simplify_cartoon( y^3-(5y/6/y)-y^3+y+(3/6/y) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at y%5E3-highlight_red%28+%285%2Ay%2F6%2Fy%29+%29-y%5E3%2By%2B%283%2F6%2Fy%29.
Remove unneeded parentheses around terms highlight_red%28+-5%2Ay%2F6%2Fy+%29
It becomes y%5E3-highlight_green%28+5%2Ay%2F6%2Fy+%29-y%5E3%2By%2B%283%2F6%2Fy%29.
Look at y%5E3-5%2Ay%2F6%2Fy-y%5E3%2By%2Bhighlight_red%28+%283%2F6%2Fy%29+%29.
Remove unneeded parentheses around terms highlight_red%28+3%2F6%2Fy+%29
It becomes y%5E3-5%2Ay%2F6%2Fy-y%5E3%2By%2Bhighlight_green%28+3%2F6%2Fy+%29.
Look at y%5E3-5%2Ay%2F6%2Fy-y%5E3%2By%2Bhighlight_red%28+3+%29%2Fhighlight_red%28+6+%29%2Fy.
Factors 3 and 6 have greatest common factor (GCF) of 3. Reducing fraction.
It becomes y%5E3-5%2Ay%2F6%2Fy-y%5E3%2By%2Bhighlight_green%28+1+%29%2Fhighlight_green%28+2+%29%2Fy.
Look at y%5E3-5%2Ahighlight_red%28+y+%29%2F6%2Fhighlight_red%28+y+%29-y%5E3%2By%2B1%2F2%2Fy.
Reduce similar several occurrences of highlight_red%28+y+%29 to
It becomes y%5E3-5%2F6-y%5E3%2By%2B1%2F2%2Fy.
Look at y%5E3-highlight_red%28+5%2F6+%29-y%5E3%2By%2B1%2F2%2Fy.
Moved -5%2F6 to the right of expression
It becomes y%5E3-y%5E3%2By%2B1%2F2%2Fy-highlight_green%28+5%2F6+%29.
Look at highlight_red%28+y%5E3+%29-highlight_red%28+y%5E3+%29%2By%2B1%2F2%2Fy-5%2F6.
Eliminated similar terms highlight_red%28+y%5E3+%29,highlight_red%28+-y%5E3+%29 replacing them with highlight_green%28+%281-1%29%2Ay%5E3+%29
It becomes highlight_green%28+%281-1%29%2Ay%5E3+%29%2By%2B1%2F2%2Fy-5%2F6.
Look at highlight_red%28+%281-1%29%2Ay%5E3+%29%2By%2B1%2F2%2Fy-5%2F6.
Since highlight_red%28+%281-1%29%2Ay%5E3+%29 has zero as a factor, it should be replaced with a zero
Look at 0%2By%2B1%2F2%2Fy-5%2F6.
Added fractions or integers together
It becomes 0%2By%2B1%2F2%2Fy-5%2F6.
Look at highlight_red%28+0+%29%2By%2B1%2F2%2Fy-5%2F6.
Remove extraneous zero highlight_red%28+0+%29
It becomes y%2B1%2F2%2Fy-5%2F6.
Result: y%2B1%2F2%2Fy-5%2F6

Universal Simplifier and Solver


Done!

Thank you,
Jojo