Question

数学作业,要过程

解下列方程..
1.(x/x-5)=(x-2)/(x-3)
2.(6x-1)/(3x+2)=(4x-7)/(2x-5)
3.{1/(x^2+5x+6)}={1/(x+2)}+{1/(x+3)}
4.解关于x的方程{(a+b)/x}+(a/b)=-1(a+b≠0)
5.解方程{[1/(x-5)]+[1/(x-9)]}={[1/(x-8)]+[1/(x-6)]}

Answer 1

1.(x/x-5)=(x-2)/(x-3)
x(x-3)=(x-2)(x-5)
x^2-3x=x^2-7x+10
4x=10
x=5/2

2.(6x-1)/(3x+2)=(4x-7)/(2x-5)
(6x-1)(2x-5)=(4x-7)(3x+2)
12x^2-32x+5=12x^2-13x-14
19x=19
x=1

3.{1/(x^2+5x+6)}={1/(x+2)}+{1/(x+3)}
{1/(x+2)(x+3)}={1/(x+2)}+{1/(x+3)}
1=(x+3)+(x+2)
2x+5=1
2x=-4
x=-2
但:x≠-2,-3
方程无解

4.解关于x的方程{(a+b)/x}+(a/b)=-1(a+b≠0)
{(a+b)/x}=-1-a/b
{(a+b)/x}=-(a+b)/b
1/x=-1/b
x=-b

5.解方程{[1/(x-5)]+[1/(x-9)]}={[1/(x-8)]+[1/(x-6)]}
{[1/(x-9)]-[1/(x-8)]}={[1/(x-6)]-[1/(x-5)]}
[(x-8)-(x-9)]/(x-8)(x-9)=[(x-5)-(x-6)]/(x-5)(x-6)
1/(x-8)(x-9)=1/(x-5)(x-6)
(x-8)(x-9)=(x-5)(x-6)
x^2-17x+72=x^2-11x+30
6x=42
x=7

Answer 2

1
(x-5)(x-2)=x(x-3)
x²-7x+10=x²-3x
-4x=-10
x=5/2

2
(3x+2)(4x-7)=(6x-1)(2x-5)
12x²-21x+8x-14=12x²-30x-2x+5
-13x-14=-32x+5
19x=19
x=1

3
1/(x²+5x+6)=1/(x+2) + 1/(x+3)
1/[(x+2)(x+3)]=1/(x+2) + 1/(x+3)
去分母
1=x+3+x+2
2x=-4
x=-2
但是x+2不能为0
所以x无解

4
(a+b)/x + a/b = -1
(a+b)/x = -1-a/b
(a+b)/x = -(a+b)/b
-x(a+b)=b(a+b)
因为a+b≠0
所以x=-b

5.
1/(x-5)+1/(x-9) = 1/(x-8)+1/(x-6)
1/(x-5)-1/(x-6)=1/(x-8)-1/(x-9)
[(x-6)-(x-5)]/[(x-5)(x-6)]=[(x-9)-(x-8)]/[(x-8)(x-9)]
-1/[(x-5)(x-6)]=-1/[(x-8)(x-9)]
所以(x-5)(x-6)=(x-8)(x-9)
x²-11x+30=x²-17x+72
6x=42
x=7

Answer 3

x/(x-5)=(x-2)/(x-3)
(x-5)(x-2)=x(x-3)
x^2-7x+10=x^2-3x
10-7x=-3x
10-4x=0
4x=10
x=2.5

(6x-1)/(3x+2)=(4x-7)/(2x-5)
(3x+2)(4x-7)=(6x-1)(2x-5)
12x^2-13x-14=12x^2-32x+5
13x+14=32x-5
19=19x
x=1
3.{1/(x^2+5x+6)}={1/(x+2)}+{1/(x+3)}
{1/(x+2)(x+3)}={1/(x+2)}+{1/(x+3)}
1=(x+3)+(x+2)
2x+5=1
2x=-4
x=-2
因为x≠-2,-3
方程无解

解关于x的方程{(a+b)/x}+(a/b)=-1(a+b≠0)
(a+b)b+ax=-bx
(a+b)b=-(ax+bx)
(a+b)b=-x(a+b)
所以(a+b)b+(a+b)x=0
(a+b)(b+x)=0
因为a+b不等于0
所以b+x=0
x=-b

.解方程{[1/(x-5)]+[1/(x-9)]}={[1/(x-8)]+[1/(x-6)]}
{[1/(x-9)]-[1/(x-8)]}={[1/(x-6)]-[1/(x-5)]}
[(x-8)-(x-9)]/(x-8)(x-9)=[(x-5)-(x-6)]/(x-5)(x-6)
1/(x-8)(x-9)=1/(x-5)(x-6)
(x-8)(x-9)=(x-5)(x-6)
x^2-17x+72=x^2-11x+30
6x=42
x=7

Answer 4

1、(x/x-5)=(x-2)/(x-3)
展开x^2-7x+10=x^2-3x
消除2次项 x=10/7

Answer 5

1.即-4（x-3)=x-2
所以5x=14
x=14/5