જો ${{2x + 3} \over {(x + 1)(x - 3)}} = {a \over {x + 1}} + {b \over {(x - 3)}}$, તો $a + b$
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b
(b) \(2x + 3 = a(x - 3) + b(x + 1)\)
(b) \(2x + 3 = a(x - 3) + b(x + 1)\)
Put \(x = - 1\); \(2( - 1) + 3 = a( - 1 - 3) \Rightarrow 1 = - 4a \Rightarrow a = {{ - 1} \over 4}\)
Now put \(x = 3\); \(2(3) + 3 = b(3 + 1)\) ==> \(9 = 4b\) ==> \(b = {9 \over 4}\)
Therefore, \(a + b = {{ - 1} \over 4} + {9 \over 4} = 2\).
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