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 explain componendo and dividendo....

Asked by Tshering Palzor...(student) , on 20/11/14


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  Componendo and dividendo is a method of simplification in mathematics.

According to it,

 text{if } frac{a}{b} = frac{c}{d} text{ and } a neq b text{, then } frac{a+b}{a-b} = frac{c+d}{c-d}.

This proof is invalid for a=b and c=d because if

 frac{a}{b} = frac{c}{d}  such that  a = b  &  d = c

then by application of componendo and dividendo we get  frac{a+b}{a-b} = frac{c+d}{c-d} = frac{a+b}{0} = frac{c+d}{0}  {a=b,c=d} and since division by zero is not defined : a neq b

Posted by Gunjan(student)

More Answers

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 plzzzzzzzzzzzzz thumbs up

Posted by Gunjan(student)

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  omponendo and dividendo is a fundamental concept in mathematics. It helps in solving complex problems.

if a / b = c / d ,  then by applying componendo and dividendo , we  get  

                   (a + b) / ( a - b ) = (c + d ) / ( c - d ), where a is not equal to b.

  This proof is invalid for a = b and c= d .

  because if a/b = c/d and a = b and c= d / then ( a+ b ) / ( a - b ) = ( c + d ) / ( c- d )

  (a+b ) / 0 = ( c+d) / 0

  which is not defined.

  componendo and dividendo is a combination of componendo and dividendo.

Proof of Componendo and Dividendo Rule

componendo rule proof

 If  a / b = c / d,

then by using componendo , we get ,

( a + b ) / b = ( c + d ) / d 

Proof: 

adding 1 both side , we get 

  a / b + 1 = c / d + 1

( a + b ) / b = ( c + d ) / d 

hence proved.

Proof of dividendo rule

If a / b = c / d , then ( a - b ) / b = ( c - d ) / d

proof: 

subtracting 1 from both side , we get

a / b - 1 = c / d - 1 

( a - b ) / b = ( c - d ) / d 

hence proved.

Proof of Componendo and Dividendo

if a / b = c / d , then ( a + b ) / ( a  - b ) = ( c + d ) / ( c - d ) 

proof : 

Taking L. H . S, we get ( a + b ) / ( a - b ) = ( a / b + 1 ) / ( a / b - 1 ) = ( c / d + 1 ) / ( c / d - 1 ) 

                                                                      = ( c + d ) / ( c - d ) 

            Hence proved.

Posted by Gunjan(student)

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 plzzzzzzzz thumbs up 

Posted by Gunjan(student)

ur effort is really appreciable.

Posted by Arshi(student)

 its all copy paste from wikipedia. we can go on it u knw

Posted by nats.arora...(student)

 according to divindo and componendo rule

a/b=c/d converts into a+b/a-b=c+d/c-d

Posted by Kenny Singh(student)

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