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Step 3 is wrong

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.

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)

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

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