I'm trying to prove this : a/b=c/d<=>(a+b)/(a−b)=(c+d)/(c−d) but going from a/b=c/d I already proved it backwards (a+b)/(a−b)=(c+d)/(c−d) I multiply each side by (a-b)(c-d) ac−ad+bc−bd=ac−bc+ad−bd so 2bc=2ad which by dividing both sides by 2bd gives us : a/b=c/d any ideas how to proceed ?

bruinhemd3ji

bruinhemd3ji

Answered question

2022-11-17

Proof of an a b = c d a + b a b = c + d c d
but going from a b = c d
I already proved it backwards
a + b a b = c + d c d I multiply each side by (a-b)(c-d)
a c a d + b c b d = a c b c + a d b d so 2 b c = 2 a d which by dividing both sides by 2 b d gives us :
a b = c d
any ideas how to proceed ?
Edit : this equivalence only works when a b and c d

Answer & Explanation

Savanna Smith

Savanna Smith

Beginner2022-11-18Added 17 answers

If q is a rational number, and a is an irrational number, then q + a is irrational, ( q + a ) a = q.
Jaslyn Sloan

Jaslyn Sloan

Beginner2022-11-19Added 6 answers

I do not think the two statements are equivalent. Take a = b = c = d = 1 then your first equality holds while the second on is undefined.

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