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[ 1/1 Equation]
    Work: Find the solution of equation （3+2/x）*（8+2/（2-x）） = 0 .
    Question type: Equation
    Solution:Original question:

(

3

+

2

÷

x

)

(

8

+

2

÷

(

2

−

x

)

)

=

0

    Remove a bracket on the left of the equation:：

3

(

8

+

2

÷

(

2

−

x

)

)

+

2

÷

x

×

(

8

+

2

÷

(

2

−

x

)

)

=

0

Multiply both sides of the equation by:

x

3

(

8

+

2

÷

(

2

−

x

)

)

x

+

2

(

8

+

2

÷

(

2

−

x

)

)

=

0

    Remove a bracket on the left of the equation:

3

×

8

x

+

3

×

2

÷

(

2

−

x

)

×

x

+

2

(

8

+

2

÷

(

2

−

x

)

)

=

0

    The equation is reduced to :

24

x

+

6

÷

(

2

−

x

)

×

x

+

2

(

8

+

2

÷

(

2

−

x

)

)

=

0

Multiply both sides of the equation by:

(

2

−

x

)

24

x

(

2

−

x

)

+

6

x

+

2

(

8

+

2

÷

(

2

−

x

)

)

(

2

−

x

)

=

0

    Remove a bracket on the left of the equation:

24

x

×

2

−

24

x

x

+

6

x

+

2

(

8

+

2

÷

(

2

−

x

)

)

(

2

−

x

)

=

0

    The equation is reduced to :

48

x

−

24

x

x

+

6

x

+

2

(

8

+

2

÷

(

2

−

x

)

)

(

2

−

x

)

=

0

    The equation is reduced to :

54

x

−

24

x

x

+

2

(

8

+

2

÷

(

2

−

x

)

)

(

2

−

x

)

=

0

    Remove a bracket on the left of the equation:

54

x

−

24

x

x

+

2

×

8

(

2

−

x

)

+

2

×

2

÷

(

2

−

x

)

×

(

2

−

x

)

=

0

    The equation is reduced to :

54

x

−

24

x

x

+

16

(

2

−

x

)

+

4

÷

(

2

−

x

)

×

(

2

−

x

)

=

0

Multiply both sides of the equation by:

(

2

−

x

)

54

x

(

2

−

x

)

−

24

x

x

(

2

−

x

)

+

16

(

2

−

x

)

(

2

−

x

)

+

4

(

2

−

x

)

=

0

    Remove a bracket on the left of the equation:

54

x

×

2

−

54

x

x

−

24

x

x

(

2

−

x

)

+

16

(

2

−

x

)

=

0

    The equation is reduced to :

108

x

−

54

x

x

−

24

x

x

(

2

−

x

)

+

16

(

2

−

x

)

(

2

−

x

)

=

0

    Remove a bracket on the left of the equation:

108

x

−

54

x

x

−

24

x

x

×

2

+

24

x

x

=

0

    The equation is reduced to :

108

x

−

54

x

x

−

48

x

x

+

24

x

x

x

=

0

    Remove a bracket on the left of the equation:

108

x

−

54

x

x

−

48

x

x

+

24

x

x

x

=

0

    The equation is reduced to :

108

x

−

54

x

x

−

48

x

x

+

24

x

x

x

=

0

    Remove a bracket on the left of the equation:

108

x

−

54

x

x

−

48

x

x

+

24

x

x

x

=

0

    The equation is reduced to :

108

x

−

54

x

x

−

48

x

x

+

24

x

x

x

=

0

    The equation is reduced to :

76

x

−

54

x

x

−

48

x

x

+

24

x

x

x

=

0

    Remove a bracket on the left of the equation:

76

x

−

54

x

x

−

48

x

x

+

24

x

x

x

=

0

    The equation is reduced to :

76

x

−

54

x

x

−

48

x

x

+

24

x

x

x

=

0

    After the equation is converted into a general formula, it is converted into:
    ( 3x + 2 )( 4x - 9 )=0
    From
        3x + 2 = 0
        4x - 9 = 0
    it is concluded that:：

x1=

-

2 3

x2=

9 4

    
    There are 2 solution(s).

解一元二次方程的详细方法请参阅：《一元二次方程的解法》

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