Question

if a:b=c:d, prove that a+b/b = c+d/d​

Answer 1

Step-by-step explanation:

Q. If (a + b + c + d) (a b c + d) = (a + b c d) (a b + c d), prove that a: b = c: d.

answer

Rewriting the given, we have

a–b–c+d

a+b+c+d

=

a–b+c–d

a+b–c–d

Now, applying componendo and dividendo

(a–b–c+d)−(a–b–c+d)

(a+b+c+d)+(a–b–c+d)

=

(a–b+c–d)−(a–b+c–d)

(a+b–c–d)+(a–b+c–d)

2(c+d)

2(a+b)

=

2(c−d))

2(a−b)

c+d

a+b

=

c−d

a−b)

a−b

a+b

=

c−d

c+d

Applying componendo and dividendo again, we get

a+b−c+b

a+b+a−b

=

c+d−c+d

c+d+c−d

2b

2a

=

2d

2c

b

a

=

d

c

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