解不等式:x^2-10x+11/x^2-2x+1≤3

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解不等式:x^2-10x+11/x^2-2x+1≤3
解不等式:x^2-10x+11/x^2-2x+1≤3

解不等式:x^2-10x+11/x^2-2x+1≤3
x^2-10x+11/x^2-2x+1≤3
(x²-10x+11-3x²+6x-3)/(x-1)²≤0
(-2x²-4x+8)/(x-1)²≤0
(x+3)(x-1)/(x-1)²≥0
因为(x-1)²≥0
分母≠0 所以x≠1
所以(x+3)(x-1)≥0
得x≥1or x≤-3
所以综上
x∈(-无穷,-3】∪(1,+无穷)