Express (11x-20)/((x-4)(x+2)) in partial fractions
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First step is to factorise the denominator
x
2
+
x
−
6
=
(
x
+
3
)
(
x
−
2
)
since these factors are linear then the numerators will be constants.
11
x
−
2
(
x
+
3
)
(
x
−
2
)
=
A
x
+
3
+
B
x
−
2
multiply both sides by (x + 3 )(x - 2 )
hence : 11x - 2 = A(x - 2 ) + B(x + 3 )..............(1)
Task now is to find A and B .Note that if x = 2 , the term with A will be zero and if x = - 3 the term with B will be zero.
let x = 2 in (1) : 20 = 5B
⇒
B
=
4
let x = -3 in (1): - 35 = - 5A
⇒
A
=
7
⇒
11
x
−
2
x
2
+
x
−
6
=
7
x
+
3
+
4
x
−
2
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