જો {{2x + 3} over {(x + 1)(x - 3)}} = {a over {x + 1}} + {b over {(x - 3)}} , તો a + b

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Basic of Logarithms

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જો ${{2x + 3} \over {(x + 1)(x - 3)}} = {a \over {x + 1}} + {b \over {(x - 3)}}$, તો $a + b$

A

$1$

B

$2$

C

$2.25$

D

$0.25$

Solution

(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, $a + b = {{ – 1} \over 4} + {9 \over 4} = 2$.

Standard 11

Mathematics

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