2022TrialShort answer

Q12 (a) (i)

2 marks

Question

Find $A$ and $B$ such that
$\frac{15}{x^2-2x-15}=\frac A{x+3}+\frac B{x-5}.$

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Solution

\frac{15}{x^2-2x-15}=\frac{A}{x+3}+\frac{B}{x-5}

15=A(x-5)+B(x+3)

Let $x=5$ :

15=B(5+3)

B=\frac{15}{8}

Let $x=-3$ :

15=A(-3-5)

A=-\frac{15}{8}

Therefore,

\frac{15}{x^2-2x-15}=-\frac{15}{8(x+3)}+\frac{15}{8(x-5)}

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Syllabus alignment

Calculus

Further IntegrationApply substitution, partial fractions, integration by parts and recurrence relationships to theoretical and practical problems.

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