SOLUTION: Simplify the rational expression {{{(3x^2-27)/(18-6x)}}}

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Question 172369: Simplify the rational expression
%283x%5E2-27%29%2F%2818-6x%29
Answer by bob123132(33) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: EXPLAIN simplification of an expression
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YOUR ANSWER


  • Graphical form: %283x%5E2-27%29%2F%2818-6x%29 simplifies to -x%2F2-3%2F2
  • Text form: (3x^2-27)/(18-6x) simplifies to -x/2-3/2
  • Cartoon (animation) form: simplify_cartoon%28+%283x%5E2-27%29%2F%2818-6x%29+%29
    For tutors: simplify_cartoon( (3x^2-27)/(18-6x) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at %283%2Ax%5E2-27%29%2F%28highlight_red%28+18+%29-6%2Ax%29.
Moved 18 to the right of expression
It becomes %283%2Ax%5E2-27%29%2F%28-6%2Ax%2Bhighlight_green%28+18+%29%29.
Look at highlight_red%28+%283%2Ax%5E2-27%29+%29%2Fhighlight_red%28+%28-6%2Ax%2B18%29+%29.
Canceled out common factors (x-(3))
Look at highlight_red%28+%283%2Ax%2B9%29%2F%28-highlight_red%28+6+%29%29+%29.
Remove unneeded parentheses around factor highlight_red%28+1%2F6+%29
It becomes -%283%2Ax%2B9%29%2Fhighlight_green%28+6+%29.
Look at -highlight_red%28+%283%2Ax%2B9%29%2F6+%29.
Expanded term -1%2F6 by using associative property on %283%2Ax%2B9%29
It becomes -highlight_green%28+1%2F6%2A3%2Ax+%29-highlight_green%28+1%2F6%2A9+%29.
Look at -1%2Fhighlight_red%28+6+%29%2Ahighlight_red%28+3+%29%2Ax-1%2F6%2A9.
Factors 3 and 6 have greatest common factor (GCF) of 3. Reducing fraction.
It becomes -1%2Fhighlight_green%28+2+%29%2Ahighlight_green%28+1+%29%2Ax-1%2F6%2A9.
Look at -highlight_red%28+1+%29%2F2%2Ahighlight_red%28+1+%29%2Ax-1%2F6%2A9.
Multiplied numerator integers
It becomes -highlight_green%28+1+%29%2F2%2Ax-1%2F6%2A9.
Look at -1%2F2%2Ax-1%2Fhighlight_red%28+6+%29%2Ahighlight_red%28+9+%29.
Factors 9 and 6 have greatest common factor (GCF) of 3. Reducing fraction.
It becomes -1%2F2%2Ax-1%2Fhighlight_green%28+2+%29%2Ahighlight_green%28+3+%29.
Look at -1%2F2%2Ax-highlight_red%28+1+%29%2F2%2Ahighlight_red%28+3+%29.
Multiplied numerator integers
It becomes -1%2F2%2Ax-highlight_green%28+3+%29%2F2.
Look at -highlight_red%28+1+%29%2F2%2Ax-3%2F2.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes -x%2F2-3%2F2.
Result: -x%2F2-3%2F2

Universal Simplifier and Solver


Done!