SOLUTION: Hi,I am having a hard time with this problem,{{{m+4}}}/{{{3m}}}x{{{4m^2}}}/{{{(m+4)(m+5)}}}...

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hi,I am having a hard time with this problem,{{{m+4}}}/{{{3m}}}x{{{4m^2}}}/{{{(m+4)(m+5)}}}...      Log On


   

Question 312840: Hi,I am having a hard time with this problem,m%2B4/3mx4m%5E2/%28m%2B4%29%28m%2B5%29...
Answer by ichudov(507) About Me  (Show Source):
You can put this solution on YOUR website!
I am guessing that you mean:
%28%28m%2B4%29%2F3m%29%2A%284m%5E2%2F%28m%2B4%29%2F%28m%2B5%29%29
just feed this to our universal simplifier as it can do those kinds of things easily:

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Graphical form: %28%28m%2B4%29%2F3%2Fm%29%2A%284m%5E2%2F%28m%2B4%29%2F%28m%2B5%29%29 simplifies to 4%2F3%2Am%2F%28m%2B5%29
  • Text form: ((m+4)/3/m)*(4m^2/(m+4)/(m+5)) simplifies to 4/3*m/(m+5)
  • Cartoon (animation) form: simplify_cartoon%28+%28%28m%2B4%29%2F3%2Fm%29%2A%284m%5E2%2F%28m%2B4%29%2F%28m%2B5%29%29+%29
    For tutors: simplify_cartoon( ((m+4)/3/m)*(4m^2/(m+4)/(m+5)) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at .
Remove unneeded parentheses around factor highlight_red%28+%28m%2B4%29+%29,highlight_red%28+1%2F3+%29,highlight_red%28+1%2Fm+%29
It becomes .
Look at .
Remove unneeded parentheses around factor highlight_red%28+4+%29,highlight_red%28+m%5E2+%29,highlight_red%28+1%2F%28m%2B4%29+%29,highlight_red%28+1%2F%28m%2B5%29+%29
It becomes .
Look at .
Reduce similar several occurrences of highlight_red%28+%28m%2B4%29+%29 to
It becomes 1%2F3%2Fm%2A4%2Am%5E2%2F%28m%2B5%29.
Look at 1%2F3%2Fhighlight_red%28+m+%29%2A4%2Ahighlight_red%28+m%5E2+%29%2F%28m%2B5%29.
Reduce similar several occurrences of highlight_red%28+1%2Fm+%29 to highlight_green%28+m%5E%28-1%2B2%29+%29
It becomes 1%2F3%2Ahighlight_green%28+m%5E%28-1%2B2%29+%29%2A4%2F%28m%2B5%29.
Look at 1%2F3%2Am%5E%28highlight_red%28+-1+%29%2B2%29%2A4%2F%28m%2B5%29.
Removed extra sign in front of -1
It becomes 1%2F3%2Am%5E%28-highlight_green%28+1+%29%2B2%29%2A4%2F%28m%2B5%29.
Look at highlight_red%28+1+%29%2F3%2Am%5E%28-1%2B2%29%2Ahighlight_red%28+4+%29%2F%28m%2B5%29.
Multiplied numerator integers
It becomes highlight_green%28+4+%29%2F3%2Am%5E%28-1%2B2%29%2F%28m%2B5%29.
Look at 4%2F3%2Am%5E%28-highlight_red%28+1+%29%2Bhighlight_red%28+2+%29%29%2F%28m%2B5%29.
Added fractions or integers together
It becomes 4%2F3%2Am%5E%28highlight_green%28+1+%29%29%2F%28m%2B5%29.
Look at 4%2F3%2Am%5Ehighlight_red%28+%281%29+%29%2F%28m%2B5%29.
Removing power of one highlight_red%28+%281%29+%29
Result: 4%2F3%2Am%2F%28m%2B5%29

Universal Simplifier and Solver


Done!