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    Maths-
    General
    Easy

    Question

    fraction numerator x plus 1 over denominator left parenthesis 2 x minus 1 right parenthesis left parenthesis 3 x plus 1 right parenthesis end fraction equals fraction numerator A over denominator 2 x minus 1 end fraction plus fraction numerator B over denominator 3 x plus 1 end fraction, then 16 A plus 9 B equals

    1. 4    
    2. 5    
    3. 6    
    4. 8    

    hintHint:

    Take LCM on LHS and simplify. Take a value of x and substitute in the simplified equation.
     

    The correct answer is: 6

       Given :
      fraction numerator x plus 1 over denominator left parenthesis 2 x minus 1 right parenthesis left parenthesis 3 x plus 1 right parenthesis end fraction equals fraction numerator A over denominator 2 x minus 1 end fraction plus fraction numerator B over denominator 3 x plus 1 end fraction

      T a k i n g space L C M space o n space L H S rightwards double arrow fraction numerator x plus 1 over denominator left parenthesis 2 x minus 1 right parenthesis left parenthesis 3 x plus 1 right parenthesis end fraction equals fraction numerator A left parenthesis 3 x space plus 1 right parenthesis space plus space B left parenthesis 2 x minus 1 right parenthesis over denominator left parenthesis 2 x minus 1 right parenthesis left parenthesis 3 x plus 1 right parenthesis end fraction rightwards double arrow x space plus space 1 space equals space A left parenthesis 3 x space plus 1 right parenthesis space plus space B left parenthesis 2 x space plus 1 right parenthesis O n space s i m p l i f y i n g rightwards double arrow x space plus space 1 space equals space A 3 x space plus space A space plus space B 2 x space minus space B rightwards double arrow x space plus space 1 space equals space A 3 x space plus space A space plus space B 2 x space minus space B rightwards double arrow x space plus space 1 space equals space A left parenthesis 3 x space plus space 1 right parenthesis space plus space B left parenthesis 2 x space minus space 1 right parenthesis T a k e space x space equals space 5 rightwards double arrow 6 space equals space 16 A space plus space 9 B space

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