SOLUTION: HELP!! Write the expression in simplest form: 4r^2-25s^2 over 2r^2+3rs-20s^2 Thank you so much!!

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Question 54397: HELP!!
Write the expression in simplest form:
4r^2-25s^2 over 2r^2+3rs-20s^2
Thank you so much!!
Found 2 solutions by Nate, funmath:
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
4r^2 - 25s^2 = (2r - 5s)(2r + 5s)
2r^2 + 3rs - 20s^2 = (r + 4s)(2r - 5s)
%28%282r+-+5s%29%282r+%2B+5s%29%29%2F%28%28r+%2B+4s%29%282r+-+5s%29%29
%282r+%2B+5s%29%2F%28r+%2B+4s%29

Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
Factor the top and bottom and cancel everything that matches between the top and the bottom (otherwise known as the numerator and denominator).
Special Factoring Pattern:highlight%28a%5E2-b%5E2=%28a%2Bb%29%28a-b%29%29
4r%5E2-25s%5E2
%282r%29%5E2-%285s%29%5E2=%282r%2B5s%29%282r-5s%29
2r%5E2%2B3rs-20s%5E2=%282r-5s%29%28r%2B4s%29
so the expression can be written as:
%282r%2B5s%29%2A%282r-5s%29%2F%28%282r-5s%29%2A%28r%2B4s%29%29
%282r%2B5s%29%2Across%282r-5s%29%2F%28cross%282r-5s%29%2A%28r%2B4s%29%29
highlight%28%282r%2B5s%29%2F%28r%2B4s%29%29
Happy Calculating!!!