After detecting the error in the following mathematical statement

3
x
2

+1

3
x
2

=1+1=2
, the correct statement obtained is ____.

Question

After detecting the error in the following mathematical statement

3
      x
      2
     
     +1
    
     3
      x
      2

=1+1=2
 , the correct statement obtained is ____.

Accepted Answer

After detecting the error in the following mathematical statement

3
      x
      2
     
     +1
    
     3
      x
      2

=1+1=2
 , the correct statement obtained is

3
      x
      2
     
     +1
    
     3
      x
      2

=1+
    1
    
     3
      x
      2

. The given mathematical statement is

3
      x
      2
     
     +1
    
     3
      x
      2

=1+1=2
 .Solve the LHS by equating LHS of question to LHS of the identity,

3
      x
      2
     
     +1
    
     3
      x
      2

=
    
     A+B
    A

That implies,

A=3
    x
    2

B=1
 Substitute the values of

A
  and

B
  in the identity,

A+B
    A
   
   =
    A
    A
   
   +
    B
    A

3
      x
      2
     
     +1
    
     3
      x
      2

=
    
     3
      x
      2

3
      x
      2

+
    1
    
     3
      x
      2

3
      x
      2
     
     +1
    
     3
      x
      2

=1+
    1
    
     3
      x
      2

Compare the given and calculated values.The Obtained answer is,

3
      x
      2
     
     +1
    
     3
      x
      2

=1+
    1
    
     3
      x
      2

Therefore, after detecting the error in the following mathematical statement

3
      x
      2
     
     +1
    
     3
      x
      2

=1+1=2
 , the correct statement obtained is

3
      x
      2
     
     +1
    
     3
      x
      2

=1+
    1
    
     3
      x
      2

.

After detecting the error in the following mathematical statement $3 x 2 + 1 3 x 2 = 1 + 1 = 2$ , the correct statement obtained is ____.

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After detecting the error in the following mathematical statement 3 x 2 +1 3 x 2 =1+1=2 , the correct statement obtained is ____.

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Detailed Solution

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After detecting the error in the following mathematical statement $3 x 2 + 1 3 x 2 = 1 + 1 = 2$ , the correct statement obtained is ____.