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Which step is wrong ...?

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Answer
    Step 3 is wrong
Explanation
Step 1:   1 = X/X
            Multiply and divided by X. 

Here Sign '/' use for horizontal fraction bar. By reverse we can again get 1, by X/X = 1. Therefore this step is true.

Step 2:     = X/1X
            Here 1 is coefficient of x denominator. 

There is always an invisible 1 as a ceefficient of a variable.
we can write X/X = X/1X = 1X/X = 1X/1X = 1. By reverse solution the answer will be still 1. This step is also true.

Step 3:     = X/1×X 
            Because 1X = 1×X 

This step is creating problem because 1X is bellow the horizontal bar is a group (product) of variable and coefficients.
All factors of a product are the coefficients of the remaining factors. e.g.; 5abc = 5bac = a5bc = abc5 etc
Similarly in ab/cd, ab is nominator and cd is denominator. If we convert ab=a*b and cd=c*d we get a*b/c*d and when further solve we get abd/c. which is wrong.


Therefore step 3 is wrong.
Step 4:     1 = X^2 

After applying these step people says that math is wrong. But they not understad their own mistakes. Please look at following image which is taken from a books written by Bartle and Sherbert.

  • Introduction to Real Analysis by Bartle and Sherbert
  • Page  42: written as 
            (x²-2)/2x
    Page  53: written as  
            1/2n = 1/(2n)
    Page 350:  written as 
            e/2M
    Page 363:  written as 
            1/n(n+1) < 1/n² <= 1/n and 
            n/(n-2)(n-1)
    

    https://www.scribd.com/doc/274935272/bartle-sherbert-real-analysis-solution-manual-pdf

    We hope this article is helpful to clear the concept. .

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    ORDER OF OPERATION ([{(-)}], ()^2 √ , ÷, ×, +, -)

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