prove componendo dividendo
Answers
Answer:
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Answer:
Proof
a
,
b
,
c
and
d
are four literals but
b
and
d
are non-zero literal numbers. Assume, the ratio of
a
to
b
is equal to the ratio of
c
to
d
.
a
b
=
c
d
Step: 1
Add one both sides of the left and right hand side fractions.
⟹
a
b
+
1
=
c
d
+
1
⟹
a
+
b
b
=
c
+
d
d
Step: 2
Subtract one both sides of the left and right hand side fractions.
⟹
a
b
−
1
=
c
d
−
1
⟹
a
−
b
b
=
c
−
d
d
Step: 3
Divide the equation obtained in step 1 by the equation obtained in step 2.
⟹
[
a
+
b
b
]
[
a
−
b
b
]
=
[
c
+
d
d
]
[
c
−
d
d
]
⟹
[
a
+
b
b
]
×
[
b
a
−
b
]
=
[
c
+
d
d
]
×
[
d
c
−
d
]
⟹
[
a
+
b
a
−
b
]
×
[
b
b
]
=
[
c
+
d
c
−
d
]
×
[
d
d
]
⟹
[
a
+
b
a
−
b
]
×
[
b
b
]
=
[
c
+
d
c
−
d
]
×
[
d
d
]
⟹
[
a
+
b
a
−
b
]
×
1
=
[
c
+
d
c
−
d
]
×
1
∴
a
+
b
a
−
b
=
c
+
d
c
−
d
Therefore, it is proved that if ratio of
a
to
b
is equal to the ratio of
c
to
d
, then the ratio of
a
+
b
to
a
−
b
is equal to the ratio of
c
+
d
to
c
−
d
. This property is called the componendo and dividendo rule.