已知3X+4Y=0(X不等于0),求分式2XY+Y的平方/X的平方-xy的值

已知3X+4Y=0(X不等于0),求分式2XY+Y的平方/X的平方-xy的值
已知3X+4Y=0(X不等于0),求分式2XY+Y的平方/X的平方-xy的值

已知3X+4Y=0(X不等于0),求分式2XY+Y的平方/X的平方-xy的值
∵3X+4Y=0 (X≠0)
∴Y=-3X/4 Y/X=-3/4
(2XY+Y²)/(X²-XY)
=Y(2X+Y)/X(X-Y)
=Y/X*(2X+Y)/(X-Y)
=-3/4*(2X-3/4X)/(X+3X/4)
=-3/4*(5X/4)/(7X/4)
=-3/4*5/4*7/4
=-105/64

∵3X+4Y=0 (X≠0)
∴Y=-3X/4 Y/X=-3/4
(2XY+Y²)/(X²-XY)
=Y(2X+Y)/X(X-Y)
=Y/X*(2X+Y)/(X-Y)
=-3/4*(2X-3/4X)/(X+3X/4)
=-3/4*(5X/4)/(7X/4)
=-3/4*5/4*7/4
=-105/64