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           ☆1 equations

[ 1/1 Equation]
    Work: Find the solution of equation -116.9+19.2*(1-1/(1+x))/x-1.8/(x*(1+x)) = 0 .
    Question type: Equation
    Solution:Original question:

-

1169 10

+

96 5

(

1

−

1

÷

(

1

+

x

)

)

÷

x

−

9 5

÷

(

x

(

1

+

x

)

)

=

0

Multiply both sides of the equation by:

x

-

1169 10

x

+

96 5

(

1

−

1

÷

(

1

+

x

)

)

−

9 5

÷

(

1

(

1

+

x

)

)

×

1

=

0

    Remove a bracket on the left of the equation:：

-

1169 10

x

+

96 5

×

1

−

96 5

×

1

÷

(

1

+

x

)

−

9 5

÷

(

1

(

1

+

x

)

)

×

1

=

0

    The equation is reduced to :

-

1169 10

x

+

96 5

−

96 5

÷

(

1

+

x

)

−

9 5

÷

(

1

(

1

+

x

)

)

=

0

Multiply both sides of the equation by:

(

1

+

x

)

-

1169 10

x

(

1

+

x

)

+

96 5

(

1

+

x

)

−

96 5

−

9 5

÷

(

1

(

1

+

x

)

)

×

(

1

+

x

)

=

0

    Remove a bracket on the left of the equation:

-

1169 10

x

×

1

−

1169 10

x

x

+

96 5

(

1

+

x

)

−

96 5

−

9 5

÷

(

1

(

1

+

x

)

)

×

(

1

+

x

)

=

0

    The equation is reduced to :

-

1169 10

x

−

1169 10

x

x

+

96 5

(

1

+

x

)

−

96 5

−

9 5

÷

(

1

(

1

+

x

)

)

×

(

1

+

x

)

=

0

Multiply both sides of the equation by:

(

1

(

1

+

x

)

)

-

1169 10

x

(

1

(

1

+

x

)

)

−

1169 10

x

x

(

1

(

1

+

x

)

)

+

96 5

(

1

+

x

)

(

1

(

1

+

x

)

)

−

96 5

(

1

(

1

+

x

)

)

=

0

    Remove a bracket on the left of the equation:

-

1169 10

x

×

1

(

1

+

x

)

−

1169 10

x

x

(

1

(

1

+

x

)

)

+

96 5

(

1

+

x

)

(

1

(

1

+

x

)

)

−

96 5

=

0

    The equation is reduced to :

-

1169 10

x

(

1

+

x

)

−

1169 10

x

x

(

1

(

1

+

x

)

)

+

96 5

(

1

+

x

)

(

1

(

1

+

x

)

)

−

96 5

(

1

(

1

+

x

)

)

=

0

    Remove a bracket on the left of the equation:

-

1169 10

x

×

1

−

1169 10

x

x

−

1169 10

x

x

(

1

(

1

+

x

)

)

+

96 5

(

1

+

x

)

=

0

    The equation is reduced to :

-

1169 10

x

−

1169 10

x

x

−

1169 10

x

x

(

1

(

1

+

x

)

)

+

96 5

(

1

+

x

)

(

1

(

1

+

x

)

)

=

0

    Remove a bracket on the left of the equation:

-

1169 10

x

−

1169 10

x

x

−

1169 10

x

x

×

1

(

1

+

x

)

+

96 5

(

1

+

x

)

=

0

    The equation is reduced to :

-

1169 10

x

−

1169 10

x

x

−

1169 10

x

x

(

1

+

x

)

+

96 5

(

1

+

x

)

(

1

(

1

+

x

)

)

=

0

    Remove a bracket on the left of the equation:

-

1169 10

x

−

1169 10

x

x

−

1169 10

x

x

×

1

−

1169 10

x

x

=

0

    The equation is reduced to :

-

1169 10

x

−

1169 10

x

x

−

1169 10

x

x

−

1169 10

x

x

x

=

0

    Remove a bracket on the left of the equation:

-

1169 10

x

−

1169 10

x

x

−

1169 10

x

x

−

1169 10

x

x

x

=

0

    The equation is reduced to :

-

1169 10

x

−

1169 10

x

x

−

1169 10

x

x

−

1169 10

x

x

x

=

0

    Remove a bracket on the left of the equation:

-

1169 10

x

−

1169 10

x

x

−

1169 10

x

x

−

1169 10

x

x

x

=

0

    The equation is reduced to :

-

1169 10

x

−

1169 10

x

x

−

1169 10

x

x

−

1169 10

x

x

x

=

0

    Remove a bracket on the left of the equation:

-

1169 10

x

−

1169 10

x

x

−

1169 10

x

x

−

1169 10

x

x

x

=

0

    The equation is reduced to :

-

1169 10

x

−

1169 10

x

x

−

1169 10

x

x

−

1169 10

x

x

x

=

0

    The equation is reduced to :

-

977 10

x

−

1169 10

x

x

−

1169 10

x

x

−

1169 10

x

x

x

=

0

    the solutions is:
        x≈-0.816908 , keep 6 decimal places    
    There are 1 solution(s).

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