Fsc Part 1 Mathematics (Complete Solution)

Q4
Prove the following rules of addition

(i)
a
c
+
b
c
=
a + b
c

SOLUTION:

L.H.S =
a
c
+
b
c
=
1 x a
c
+
1 x b
c
=
1 (a + b)
c
(Right dist. property)
=
a + b
c
= R.H.S
(ii)
a
b
+
c
d
=
ad + bc
bd
SOLUTION:
L.H.S =
a
b
+
c
d
= 1 x
a
b
+ 1 x
c
d
= ( d x
1
d
) x
a
b
+ ( b x
1
b
) x
c
d
= ad x
1
bd
+ bc x
1
bd
= (ad + bc) x
1
bd
=
ad + bc
bd
= R.H.S

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