解不等式3x-5/x²+2x-3≤2
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3x-5/x²+2x-3≤2
(3x-5)/(x²+2x-3)-2(x²+2x-3)/(x²+2x-3)≤0
(3x-5-2x²-4x+6)/(x²+2x-3)<=0
(-2x²-x+1)/(x²+2x-3)<=0
(2x²+x-1)/(x²+2x-3)>=0
(x+1)(2x-1)/(x+3)(x-1)>=0
即
(x+3)(x+1)(2x-1)(x-1)>=0
(x+3)(x-1)≠0
所以
x>1或-1<=x<=1/2或x<-3
(3x-5)/(x²+2x-3)-2(x²+2x-3)/(x²+2x-3)≤0
(3x-5-2x²-4x+6)/(x²+2x-3)<=0
(-2x²-x+1)/(x²+2x-3)<=0
(2x²+x-1)/(x²+2x-3)>=0
(x+1)(2x-1)/(x+3)(x-1)>=0
即
(x+3)(x+1)(2x-1)(x-1)>=0
(x+3)(x-1)≠0
所以
x>1或-1<=x<=1/2或x<-3
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