If a/c and b/c and (a,b) =d prove that ab/cd Solution a/b = c/d Adding and subtracting 1 to both sides, a/b + 1 = c/d + 1 and a/b - 1 = c/d -1 => (a+b)/b = (c+d)/d ... (1) and (a-b)/b = (c-d)/d ... (2) Dividing equation (1) by equation (2), => (a+b)/(a-b) = (c+d)/(c-d) .

1. If a/c and b/c and (a,b) =d prove that ab/cd
Solution
a/b = c/d
Adding and subtracting 1 to both sides,
a/b + 1 = c/d + 1 and a/b - 1 = c/d -1
=> (a+b)/b = (c+d)/d ... (1)
and (a-b)/b = (c-d)/d ... (2)
Dividing equation (1) by equation (2),
=> (a+b)/(a-b) = (c+d)/(c-d)