Question 116927
{{{((21x^2-20xy+4y^2)/(28x^2+27xy-10y^2))/((15x^2-19xy+6y^2)/(10x^2+9xy-9y^2))}}} Start with the given expression



{{{((21x^2-20xy+4y^2)/(28x^2+27xy-10y^2))((10x^2+9xy-9y^2)/(15x^2-19xy+6y^2))}}}  Multiply the first fraction by the reciprocal of the second fraction                                                           


{{{(((3x-2y)(7x-2y))/(28x^2+27xy-10y^2))((10x^2+9xy-9y^2)/(15x^2-19xy+6y^2))}}}   Factor {{{21x^2-20xy+4y^2}}} to get {{{(3x-2y)(7x-2y)}}} 


{{{(((3x-2y)(7x-2y))/((4x+5y)(7x-2y)))((10x^2+9xy-9y^2)/(15x^2-19xy+6y^2))}}}   Factor {{{28x^2+27xy-10y^2}}} to get {{{(4x+5y)(7x-2y)}}} 


{{{(((3x-2y)(7x-2y))/((4x+5y)(7x-2y)))(((2x+3y)(5x-3y))/(15x^2-19xy+6y^2))}}}   Factor {{{10x^2+9xy-9y^2}}} to get {{{(2x+3y)(5x-3y)}}} 


{{{(((3x-2y)(7x-2y))/((4x+5y)(7x-2y)))(((2x+3y)(5x-3y))/((3x-2y)(5x-3y)))}}}   Factor {{{15x^2-19xy+6y^2}}} to get {{{(3x-2y)(5x-3y)}}} 



{{{(3x-2y)(7x-2y)(2x+3y)(5x-3y)/(4x+5y)(7x-2y)(3x-2y)(5x-3y)}}} Combine the fractions



{{{cross((3x-2y))cross((7x-2y))(2x+3y)cross((5x-3y))/(4x+5y)cross((7x-2y))cross((3x-2y))cross((5x-3y))}}} Cancel like terms



{{{(2x+3y)/(4x+5y)}}} Simplify



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Answer:


So {{{((21x^2-20xy+4y^2)/(28x^2+27xy-10y^2))((10x^2+9xy-9y^2)/(15x^2-19xy+6y^2))}}} simplifies to {{{(2x+3y)/(4x+5y)}}}. In other words {{{((21x^2-20xy+4y^2)/(28x^2+27xy-10y^2))((10x^2+9xy-9y^2)/(15x^2-19xy+6y^2))=(2x+3y)/(4x+5y)}}}