(a²+ab)÷（a²-b²）
=a(a+b)÷[(a-b)(a+b)]
=a÷(a-b)
=a/(a+b)
.已知a²-4a+9b²+6b+5=0,求1/a-1/b的值
a²-4a+9b²+6b+5=0
a²-4a+4+9b²+6b+1=0
(a-2)²+(3b+1)²=0
(a-2)²=0,(3b+1)²=0
a=2,b=-1/3
1/a-1/b
=1/2-1/(-1/3)
=1/2+3
=7/2
3.已知x²
4.已知x+1/x=3,求x²÷(x四次方+x²+1）的值
x^2÷(x^4+x^2+1)取倒数
(x^4+x^2+1)÷x^2
=x^2+1+1/x^2
=x^2+2+1/x^2-1
=(x+1/x^2)^2-1
=3^2-1
=9-1
=8
再取倒数
x^2÷(x^4+x^2+1)=1/8