Let $$\(\mathrm{f}(x)=\frac{5 a}{(2 x-a)(3 a-x)}\)$$, where $$\(a\)$$ is a positive constant. Express $$\(\mathrm{f}(x)\)$$ in partial fractions. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics
IGCSE&ALevel
CAIE
Exam No:9709_m21_qp_32 Year:2021 Question No:6(a)

Answer:

Carry out a relevant method to determine constants \(A\) and \(B\) such that
\(\frac{5 a}{(2 x-a)(3 a-x)}=\frac{A}{2 x-a}+\frac{B}{3 a-x}\)
Obtain \(A=2\)
Obtain \(B=1\)

Knowledge points:

3.1.4.1 (ax + b)(cx + d)(ex + f)

Solution:

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