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    Maths-
    General
    Easy

    Question

    If fraction numerator x to the power of 2 end exponent minus 10 x plus 13 over denominator left parenthesis x minus 1 right parenthesis open parentheses x to the power of 2 end exponent minus 5 x plus 6 close parentheses end fraction equals fraction numerator A over denominator x minus 1 end fraction plus fraction numerator B over denominator x minus 2 end fraction plus fraction numerator K over denominator x minus 3 end fraction then K=

    1. -1    
    2. -2    
    3. -3    
    4. -4    

    hintHint:

    • Take LCM on RHS and simplify
    • Then take a value of x which satisfies the requirement.

    The correct answer is: -4

       Given :
      fraction numerator x to the power of 2 end exponent minus 10 x plus 13 over denominator left parenthesis x minus 1 right parenthesis open parentheses x to the power of 2 end exponent minus 5 x plus 6 close parentheses end fraction equals fraction numerator A over denominator x minus 1 end fraction plus fraction numerator B over denominator x minus 2 end fraction plus fraction numerator K over denominator x minus 3 end fraction

      Taking LCM on RHS and factorizing on LHS
      rightwards double arrow fraction numerator x squared minus 10 x plus 13 over denominator left parenthesis x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis left parenthesis x minus 3 right parenthesis end fraction equals fraction numerator A left parenthesis x minus 2 right parenthesis left parenthesis x minus 3 right parenthesis space plus space B left parenthesis x minus 1 right parenthesis left parenthesis x minus 3 right parenthesis space plus space K left parenthesis x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis over denominator left parenthesis x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis left parenthesis x minus 3 right parenthesis end fraction rightwards double arrow x squared minus 10 x plus 13 space equals space A left parenthesis x squared space minus 5 x space plus 6 right parenthesis plus space B left parenthesis x squared minus 4 x space plus 3 right parenthesis space plus space K left parenthesis x squared space minus 3 x space plus 2 right parenthesis rightwards double arrow x squared minus 10 x plus 13 space equals space A left parenthesis x minus 2 right parenthesis left parenthesis x minus 3 right parenthesis space plus space B left parenthesis x minus 1 right parenthesis left parenthesis x minus 3 right parenthesis space plus space K left parenthesis x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis P u t space x equals space 3 rightwards double arrow 9 minus 30 plus 13 space equals space 0 plus 0 right parenthesis space plus space 2 K rightwards double arrow 2 K space equals space minus 8 rightwards double arrow space K space equals space minus 4
       

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