Question

化简：1.（x²-4/x²-4x+4-x-2/x+2）÷x/x-2

2.（a+2/a²-2a-a-1/a²-4a+4）÷4-a/a²-2a
3. x²+9x/x²+3x+x²-9/x²+6x+9
解方程
1.x+1/x-1-4/x²-1=1
2.1/x+2+1/x=32/x²+2x
3.3x+4/3x-5+1=4x+1/2x-3

Answer 1

.（x²-4/x²-4x+4-x-2/x+2）÷x/x-2
=[(x-2)(x+2)/(x-2)²-(x-2)/(x+2)]÷x/(x-2)
=[(x+2)/(x-2)-(x-2)/(x+2)]*(x-2)/x
=(x²+4x+4-x²+4x-4)/(x-2)(x+2)*(x-2)/x
=8/(x+2)

2.（a+2/a²-2a-a-1/a²-4a+4）÷4-a/a²-2a
=[(a+2)/a(a-2)-(a-1)/(a-2)²]÷(4-a)/a(a-2)
=(a²-4-a²+a)/a(a-2)²×a(a-2)/(4-a)
=-1/(a-2)
=1/(2-a)

3. x²+9x/x²+3x+x²-9/x²+6x+9
=x(x+9)/x(x+3)+(x-3)(x+3)/(x+3)²
=x(x+9)/x(x+3)+(x-3)/(x+3)
=(x²+9x+x²-3x)/x(x+3)
=2x(x+3)/x(x+3)
=2

1.x+1/x-1-4/x²-1=1
(x+1)²-4=x²-1
x²+2x+1-4=x²-1
2x=2
x=1
∵x=1原方程无意义
∴原方程无解

2.1/x+2+1/x=32/x²+2x
x+x+2=32
2x=30
x=15

3.3x+4/3x-5+1=4x+1/2x-3
(3x+4)(2x-3)+(3x-5)(2x-3)=(4x+1)(3x-5)
6x²-x-12+6x²-19x+15=12x²-17x-5
12x²-20x-12x²+17x=-5-3
-3x=-8
x=8/3

雪菲，又是你。