Question

If a/b = c/d , prove that (3a - 5b)/(3a + 5b) = (3c - 5d)/(3c + 5d)
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Answer 1

Step-by-step explanation:

Given :-

a/b = c/d

To find :-

Prove that (3a - 5b)/(3a + 5b) = (3c - 5d)/(3c + 5d)

Solution :-

Given that :

a/b = c/d

On multiplying with 3/5 both sides then

=> (3/5)(a/b) = (3/5)(c/d)

=> (3×a)/(5×b) = (3×c)/(5×d)

=> 3a/5b = 3c/5d

We know that Componendo and dividendo

=> (3a+5b)/(3a-5b) = (3c+5d)/(3c-5d)

=> (3a-5b)/(3a+5b) = (3c-5d)/(3c+5d)

by Alternendo

Hence, Proved.

(or )

Given that :

a/b = c/d

On multiplying with 3/5 both sides then

=> (3/5)(a/b) = (3/5)(c/d)

=> (3×a)/(5×b) = (3×c)/(5×d)

=> 3a/5b = 3c/5d -----------(1)

On adding 1 both sides then

=> (3a/5b)+1 = (3c/5d)+1

=> (3a+5b)/5b = (3c+5d)/5d ------(2)

On subtracting 1 from both sides then

=> (3a/5b)-1 = (3c/5d)-1

=> (3a-5b)/5b = (3c-5d)/5d ------(3)

On dividing (3) by (2) then

[(3a-5b)/5b]/[(3a+5b)/5b]= [(3c-5d)/5d]/[(3c+5d)/5d]

=> (3a-5b)/(3a+5b) = (3c-5d)/(3c+5d)

Hence, Proved.

Answer :-

If a/b = c/d then

(3a - 5b)/(3a + 5b) = (3c - 5d)/(3c + 5d)

Used formulae:-

Componendo and dividendo:-

If a :b = c:d then (a+b):(a-b) = (c+d):(c-d)

In words if the 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.

Answer 2

Step-by-step explanation:

Question :

If $\bold{\dfrac{a}{b}=\dfrac{c}{d} }$, prove that $\bold{\dfrac{3a-5b}{3a+5b}=\dfrac{3c-5d}{3c+5d} }$.

Solution :

$\rightarrow \bold{\dfrac{a}{b}=\dfrac{c}{d} =\dfrac{3a}{5b}=\dfrac{3c}{5d} }$

[ Multiplying 3/5 on both sides ]

$\rightarrow \bold{\dfrac{3a+5b}{3a-5b}=\dfrac{3c+5d}{3c-5d} }$

[ By componendo & dividendo ]

$\rightarrow \bold{\dfrac{3a-5b}{3a+5b}=\dfrac{3c-5d}{3c+5d} }$

[ By invertendo ]

Hence, $\bold{\dfrac{3a-5b}{3a+5b}=\dfrac{3c-5d}{3c+5d} }$.

Learn more :

a/b = c/d ⟹ b/a = d/c [Invertendo]

a/b = c/d ⟹ a/c = b/d [Alternendo]

a/b = c/d ⟹ (a + b)/b = (c + d)/d [Componendo]

a/b = c/d ⟹ )a - b)/b = (c - d)/d [Dividendo]

a/b = c/d ⟹ (a + b)/(a - b) = (c + d)/(c - d) [Componendo & Dividendo]

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