SOLUTION: Write the expression in simplest form. 4r^2-25s^2 ----------- --- 2r^2+3rs-20s^2 I have tried to work this problem, over and over again, but can not figure it o

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Write the expression in simplest form. 4r^2-25s^2 ----------- --- 2r^2+3rs-20s^2 I have tried to work this problem, over and over again, but can not figure it o      Log On


   

Question 64921: Write the expression in simplest form.
4r^2-25s^2
---------------
2r^2+3rs-20s^2
I have tried to work this problem, over and over again, but can not figure it out. The best I can come up with is -3/3rs-4. I hope that someone out there can help me, because I do not have any more hair to pull out. Thanks.
Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
FACTORING THE NUMERATOR WE GET
4R^2-25S^2=(2R-5S)(2R+5S)
NOW FACTOR THE DENOMINATOR WE GET
(2R-5S)(R+4S)
NOW WE CANCEL OUT THE COMMON TERM (2R-5S) & WE HAVE LEFT
(2R+5S)/(R+4S)
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LETS TRY SOME SIMPLE EXAMPLES:
X^2-25=0 WHEN YOU HAVE A SECOND POWER UNKNOWN (X^2) & A NEGATIVE SQUARE(-25)
TAKE THE SQUARE ROOT OF BOTH TERMS x & 5:
NOW GROUP THESE TWO FACTORS WITH A (+) & A (-) SIGN THUS:
(X+5)(X-5) EXPANDING THESE FACTORS WE HAVE (X*X=X^2) & (5*-5=-25) THE NORMAL MIDDLE TERMS CANCEL EACH OTHER OUT (5X-5X=0)
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HOPE THIS HELPS,
IF YOU NEED ADDITIONAL EXAMPLES -- PLEASE ASK.