Proportion Entailment

Question

Given: a/b = c/d

Prove: a/b = a+c/b+d

Answer 1

Since a/b = c/d, ad = bc

 

a(b+d) = ab + ad

 

           = ab + bc

 

           = b(a+c)

 

So, a(b+d) = b(a+c)

 

Divide both sides by b(b+d) to obtain a/b = (a+c)/(b+d)