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Mathematics
If (1/(3-5x)(2+3x))= (A/3-5x)+ (B/2+3x) then A: B is .................
Q. If
(
3
−
5
x
)
(
2
+
3
x
)
1
=
3
−
5
x
A
+
2
+
3
x
B
then
A
:
B
is .................
1708
262
KCET
KCET 2010
Integrals
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A
3 : 5
20%
B
3 : 2
29%
C
2 : 3
21%
D
5 : 3
30%
Solution:
Given,
(
3
−
5
x
)
(
2
+
3
x
)
1
=
(
3
−
5
x
)
A
+
(
2
+
3
x
)
B
By partial fraction
1
=
(
3
A
−
5
B
)
x
+
(
2
A
+
3
B
)
On comparing the like powers of '
x
'
3
A
−
5
B
=
0
...(i)
and
2
A
+
3
B
=
1
...(ii)
On solving, we get
A
=
19
5
,
B
=
19
3
Hence,
A
:
B
=
5
:
3