Question

(a-b)(c-d)/(b-c)(d-a) =2012/2013

Find value of (a-c)(b-d)/(a-b)(c-d)

Answer 1

As gcd(2012,2013)=1

(a-b)(c-d)=2012

(b-c)(d-a)=2013=(a-b)(c-d)+1

bd+ac-ab-cd=ac+bd-ad-bc+1

a(d-b)+c(b-d)=1

(a-c)(b-d)=-1

(a-c)(b-d)/(a-b)(c-d)= -1/2012

That's your answer.