已知X/Y=4/3,求(3X^2-5XY+2Y^2)/(2X^2+3XY-5Y^2)的值 "

X/Y=4/3,
X=4Y/3,
(3X^2-5XY+2Y^2)/(2X^2+3XY-5Y^2)
=(X-Y)(3X-2Y)/[(X-Y)(2X+5Y)]
=(3X-2Y)/(2X+5Y)
=[3*(4Y/3)-2Y]/[2*(4Y/3)+5Y]
=2Y/(23Y/3)
=6/23.

x/y=4/3
x=4y/3
3x^2-5xy+2y^2
=3*(4y/3)^2-5(4y/3)y+2y^2
=2y^2/3
2x^2+3xy-5y^2
=2(4y/3)^2+3(4y/3)y-5y^2
=23y^2/9
所以原式=(2y^2/3)/(23y^2/9)=6/23

x=4/3y
然后带入后面那个式子
=(16/3Y^2-20/3Y^2+2Y^2)/(32/9Y^2+4Y^2-5Y^2)
=6/23