SOLUTION: Adding/Subtracting rational expressions y^3 - 5y/6y - y^3 + y + 3/6y

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Question 173558: Adding/Subtracting rational expressions
y^3 - 5y/6y - y^3 + y + 3/6y
Answer by bob123132(33) About Me  (Show Source):
You can put this solution on YOUR website!
You need to multiply each by the LCD: which is 6y. You will need to multiply the numerator by it for only the whole number: ex. you multiply the y^3 by 6y because it has no fraction but on the other hand do not multiply the tops of the ones with the 6y as their denominator. You should end up with
%286y%5E4-5y-6y%5E4%2B6y%5E2%2B3%29%2F6y+
Then further simplify:
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Graphical form: %286y%5E4-5y-6y%5E4%2B6y%5E2%2B3%29%2F6%2Fy simplifies to %28-5%2Ay%2B6%2Ay%5E2%2B3%29%2F6%2Fy
  • Text form: (6y^4-5y-6y^4+6y^2+3)/6/y simplifies to (-5*y+6*y^2+3)/6/y
  • Cartoon (animation) form: simplify_cartoon%28+%286y%5E4-5y-6y%5E4%2B6y%5E2%2B3%29%2F6%2Fy+%29
    For tutors: simplify_cartoon( (6y^4-5y-6y^4+6y^2+3)/6/y )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at .
Eliminated similar terms highlight_red%28+6%2Ay%5E4+%29,highlight_red%28+-6%2Ay%5E4+%29 replacing them with highlight_green%28+%286-6%29%2Ay%5E4+%29
It becomes %28highlight_green%28+%286-6%29%2Ay%5E4+%29-5%2Ay%2B6%2Ay%5E2%2B3%29%2F6%2Fy.
Look at %28highlight_red%28+%286-6%29%2Ay%5E4+%29-5%2Ay%2B6%2Ay%5E2%2B3%29%2F6%2Fy.
Since highlight_red%28+%286-6%29%2Ay%5E4+%29 has zero as a factor, it should be replaced with a zero
Look at %280-5%2Ay%2B6%2Ay%5E2%2B3%29%2F6%2Fy.
Added fractions or integers together
It becomes %280-5%2Ay%2B6%2Ay%5E2%2B3%29%2F6%2Fy.
Look at %28highlight_red%28+0+%29-5%2Ay%2B6%2Ay%5E2%2B3%29%2F6%2Fy.
Remove extraneous zero highlight_red%28+0+%29
It becomes %28-5%2Ay%2B6%2Ay%5E2%2B3%29%2F6%2Fy.
Result: %28-5%2Ay%2B6%2Ay%5E2%2B3%29%2F6%2Fy

Universal Simplifier and Solver


Done!