x^2 + 13x + 15 (2x + 3) , (x + 3) ^2 = - Vidyadip

MCQ

${{{x^2} + 13x + 15} \over {(2x + 3)\,{{(x + 3)}^2}}} = $

✓
${1 \over {x + 3}} - {1 \over {2x + 3}} + {5 \over {{{(x + 3)}^2}}}$
B
${1 \over {2x + 3}} - {1 \over {x + 3}} + {5 \over {{{(x + 3)}^2}}}$
C
${1 \over {2x + 3}} + {1 \over {x + 3}} - {5 \over {{{(x + 3)}^2}}}$
D
${1 \over {2x + 3}} - {1 \over {x + 3}} - {5 \over {{{(x + 3)}^2}}}$

✓

Answer

Correct option: A.

${1 \over {x + 3}} - {1 \over {2x + 3}} + {5 \over {{{(x + 3)}^2}}}$

a
(a) ${{{x^2} + 13x + 15} \over {(2x + 3)\,{{(x + 3)}^2}}} = {A \over {2x + 3}} + {B \over {x + 3}} + {C \over {{{(x + 3)}^2}}}$

==> ${x^2} + 13x + 15 = A{(x + 3)^2} + B(2x + 3)\,(x + 3) + C(2x + 3)$

For $x = - 3,\,C = 5$ and for $x = - {3 \over 2};\,A = - 1$

Equating coefficient of ${x^2}$

$1 = A + 2B \Rightarrow B = {{1 - A} \over 2} = 1$

$\therefore $ Given expression = ${1 \over {x + 3}} - {1 \over {2x + 3}} + {5 \over {{{(x + 3)}^2}}}$.

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