Question

Can somebody please explain th3 attached to me. is there a proof or something???

Answer 1

just think about it, it will come to you.

Answer 2

@koalamon now about a hint

Answer 3

hint: in this equation:\[\frac{a+b}{a-b}=\frac{c+d}{c-d}\]divide the numerator and denominator of the left-hand-side by 'b' and divide the numerator and denominator of the right-hand-side by 'd'.

Answer 4

@asnaseer, even after your hint, i am still running into difficulty

Answer 5

Isn't this Componendo & Dividendo? ;)

Answer 6

what is componedo and dividendo???

Answer 7

It is a theorem in which the denominator is added to the numerator & numerator is added with negative denominator e. g.
if \[\frac{x}{y}=\frac{a}{b}\] then by componendo & dividendo we have
\[\frac{( x + y)}{( x- y ) }\]= \[\frac{( a +b )}{( a - b )}\]
(Proof)
\[\frac{3}{2}\] =\[\frac{ 6}{4}\] then by componendo & dividendo
\[\frac{3+ 2}{3-2}\] = \[\frac{6 +4}{6- 4}\]
OR 5/ 1 = 10/ 2 that is true

Answer 8

@DLS do you understand asnaseer's hint???

Answer 9

I think the theorem is better,
he just said if u do the same thing/operation with a digit on one side,u do that on other too so overall effect nullifies

Answer 10

you helped me greatly thanks

Answer 11

This is what I meant - starting with this:\[\frac{a+b}{a-b}=\frac{c+d}{c-d}\]lets first divide the numerator and denominator of the left-hand-side by 'b' to give:\[\frac{\frac{a}{b}+1}{\frac{a}{b}-1}=\frac{c+d}{c-d}\]then lets divide the numerator and denominator of the right-hand-side by 'd' to give:\[\frac{\frac{a}{b}+1}{\frac{a}{b}-1}=\frac{\frac{c}{d}+1}{\frac{c}{d}-1}\]now note that you are given that:\[\frac{a}{b}=\frac{c}{d}\]so the equality of both sides follows from this relation.

Answer 12

I don't think you can just assume the "Componendo and dividendo" theorem directly as this question is effectively asking you to prove it.