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Manipal Engineering Manipal Engineering Solved Paper-2011

  • question_answer
    If\[\frac{2x+3}{(x+1)(x-3)}=\frac{a}{x+1}+\frac{b}{x-3}\], then\[a+b\]is equal to

    A) \[1\]                                     

    B) \[2\]

    C) \[9/4\]                 

    D)        \[-1/4\]

    Correct Answer: B

    Solution :

    Given that,                 \[\frac{2x+3}{(x+1)(x-3)}=\frac{a}{(x+1)}+\frac{b}{(x-3)}\] \[\Rightarrow \]               \[(2x+3)=a(x-3)+b(x+1)\] On comparing the coefficient of\[x\]and constant, we get                 \[2=a+b\]and\[3=-3a+b\] \[\Rightarrow \]               \[a=-\frac{1}{4}\]and\[b=\frac{9}{4}\] \[\therefore \]  \[a+b=-\frac{1}{4}+\frac{9}{4}=2\]


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