2-3x/x^2-x+1>3 分式不等式

原式=[1/(x-3)(x-4) +2/(x-1)(x-3) ]×(x-4)(x-1)/3x
=[(x-1)+2(x-4)]/(x-1)(x-3)(x-4) ×(x-4)(x-1)/3x
=(3x-9)/(x-3) ×1/3x
=3(x-3)/(x-3) ×1/3x
=1/x

原式=[x(x-3)/(x-3)²][(x-5)(x-6)/x(x-5)]-1
=[x/(x-3)][(x-6)/x]-1
=(x-6)/(x-3)-1
=(x-6-x+3)/(x-3)
=-3/(x-3)

1、(a-b)/a(a+b) ×a²(a+b)(a-b)/[-a(a-b)]
=-(a-b)
=b-a
2、x(x-3)/(x-3)²×(x-5)(x-6)/x(x-5)
=(x-6)/(x-3)
3、-(x+4)(x-4)/(x-3)(x+1)×(x-3)/(x-1)(x-4)
=-(x+4)/(x+1)(x-1)
=(x+4)/(1-x²)

原式=3x/(x-3)²×[-(x-3)/x]
=-3x/(x-3)²×(x-3)/x
=-3/(x-3)

1、1/2a^2b=6bc^2/(12a^2b^2c^2)
3/4ab^2=9ac^2/(12a^2b^2c^2)
5/6ac^2=10ab^2/(12a^2b^2c^2)
2、1/x-1=(x+1)/(x^2-1)
1/x+1=(x-1)/(x^2-1)
3x/x^2-1=3x/(x^2-1)
3、x+2/x^2-2x=(x+2)(x-2)/[x(x-2)^2]
x-1/x^2-4x+4=x(x-1)/[x(x-2)^2]

分式约分a-b/a^2+ab乘a^2b^2-a^4/ab-a^2.
=(a-b)/a(a+b)×a²(b²-a²)/a(b-a)
=a-b;
x^2-3x/x^2-6x+9乘x^2-11x+30/x^2-5.
=x(x-3)/(x-3)²×(x-5)(x-6)/(x²-5)
=x(x-5)(x-6)/(x-3)(x²-5);
16-x^2/x^2-2x-3÷x^2-5x+4/x-3
=(4+x)(4-x)/(x-3)(x+1)×(x-3)/(x-1)(x-4)
=(x+4)/(1-x²);
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两边乘以(x-2)(x-5)得
3x=A(x-5)+B(x-2)
3x=(A+B)x+(-5A-2B)
∴A+B=3
-5A-2B=0
解这个方程组得
A=-2
B=5