Question

(a²+ab)÷（a²-b²）=？？ 2.已知a²-4a+9b²+6b+5=0,求1/a-1/b的值 3.已知x²

4.已知x+1/x=3,求x²÷(x四次方+x²+1）的值

Answer 1

(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

Answer 2

(a²+ab)÷（a²-b²）=a(a+b)/(a+b)(a-b)=a/(a-b)
由a²-4a+9b²+6b+5=0=（a-2)²+（3b+1)²=0从而得出a=2,b=-1/3,带入1/a-1/b=-3
求x²÷(x四次方+x²+1）可先求(x四次方+x²+1）*x²=x²+1+1/x²，由已知x+1/x=3推出x²+2+1/x²=3，进而得出x²+1+1/x²=2，从而x²÷(x四次方+x²+1）=1/（(x四次方+x²+1）*x²）=1/（x²+1+1/x²）=1/2