Question 117929

{{{(4r^2-25s^2)/(2r^2+3rs-20s^2)}}} Start with the given expression


{{{((2r+5s)(2r-5s))/(2r^2+3rs-20s^2)}}}   Factor {{{4r^2-25s^2}}} to get {{{(2r+5s)(2r-5s)}}} 


{{{((2r+5s)(2r-5s))/((r+4s)(2r-5s))}}}   Factor {{{2r^2+3rs-20s^2}}} to get {{{(r+4s)(2r-5s)}}} 



{{{(2r+5s)cross((2r-5s))/(r+4s)cross((2r-5s))}}} Cancel like terms



{{{(2r+5s)/(r+4s)}}} Simplify



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Answer:


So {{{(4r^2-25s^2)/(2r^2+3rs-20s^2)}}} simplifies to {{{(2r+5s)/(r+4s)}}}. In other words {{{(4r^2-25s^2)/(2r^2+3rs-20s^2)=(2r+5s)/(r+4s)}}}