优质解答

1/2x=2/x+3

对角相乘

4x=x+3

3x=3

x=1

分式方程要检验

经检验,x=1是方程的解

x/(x+1)=2x/(3x+3)+1

两边乘3(x+1)

3x=2x+(3x+3)

3x=5x+3

2x=-3

x=-3/2

分式方程要检验

经检验,x=-3/2是方程的解

2/x-1=4/x^2-1

两边乘(x+1)(x-1)

2(x+1)=4

2x+2=4

2x=2

x=1

分式方程要检验

经检验,x=1使分母为0,是增根,舍去

所以原方程无解

5/x^2+x - 1/x^2-x=0

两边乘x(x+1)(x-1)

5(x-1)-(x+1)=0

5x-5-x-1=0

4x=6

x=3/2

分式方程要检验

经检验,x=3/2是方程的解

5x/(3x-4)=1/(4-3x)-2

乘3x-4

5x=-1-2(3x-4)=-1-6x+8

11x=7

x=7/11

分式方程要检验

经检验

x=7/11是方程的解

1/(x+2) + 1/(x+7) = 1/(x+3) + 1/(x+6)

通分

(x+7+x+2)/(x+2)(x+7)=(x+6+x+3)/(x+3)(x+6)

(2x+9)/(x^2-9x+14)-(2x+9)/(x^2+9x+18)=0

(2x+9)[1/(x^2-9x+14)-1/(x^2+9x+18)]=0

因为x^2-9x+14不等于x^2+9x+18

所以1/(x^2-9x+14)-1/(x^2+9x+18)不等于0

所以2x+9=0

x=-9/2

分式方程要检验

经检验

x=-9/2是方程的解

7/(x^2+x)+1/(x^2-x)=6/(x^2-1)

两边同乘x(x+1)(x-1)

7(x-1)+(x+1)=6x

8x-6=6x

2x=6

x=3

分式方程要检验

经检验,x=3是方程的解

化简求值.[X-1-(8/X+1)]/[X+3/X+1] 其中X=3-根号2

[X-1-(8/X+1)]/[(X+3)/(X+1)]

={[(X-1)(X+1)-8]/(X+1)}/[(X+3)/(X+1)]

=(X^2-9)/(X+3)

=(X+3)(X-3)/(X+3)

=X-3

=-根号2

8/(4x^2-1)+(2x+3)/(1-2x)=1

8/(4x^2-1)-(2x+3)/(2x-1)=1

8/(4x^2-1)-(2x+3)(2x+1)/(2x-1)(2x+1)=1

[8-(2x+3)(2x+1)]/(4x^2-1)=1

8-(4x^2+8x+3)=(4x^2-1)

8x^2+8x-6=0

4x^2+4x-3=0

(2x+3)(2x-1)=0

x1=-3/2

x2=1/2

代入检验,x=1/2使得分母1-2x和4x^2-1=0.舍去

所以原方程解:x=-3/2

(x+1)/(x+2)+(x+6)/(x+7)=(x+2)/(x+3)+(x+5)/(x+6)

1-1/(x+2)+1-1/(x+7)=1-1/(x+3)+1-1/(x+6)

-1/(x+2)-1/(x+7)=-1/(x+3)-1/(x+6)

1/(x+2)+1/(x+7)=1/(x+3)+1/(x+6)

1/(x+2)-1/(x+3)=1/(x+6)-1/(x+7)

(x+3-(x+2))/(x+2)(x+3)=(x+7-(x+6))/(x+6)(x+7)

1/(x+2)(x+3)=1/(x+6)(x+7)

(x+2)(x+3)=(x+6)(x+7)

x^2+5x+6=x^2+13x+42

8x=-36

x=-9/2

经检验,x=-9/2是方程的根.

(2-x)/(x-3)+1/(3-x)=1

(2-x)/(x-3)-1/(x-3)=1

(2-x-1)/(x-3)=1

1-x=x-3

x=2

分式方程要检验

经检验,x=2是方程的根