If `(a+b)/(b+c) = (c +d)/(d + a)` , that prove that ` c = a " or, " a + b + c + d = 0`.

Explanation

Given that ` (a+b)/(b +c) = (c +d)/(d + a)`
or, ` (a + b - b - c)/(b + c) = (c + d - d - a)/(d + a)` [by dividendo]
or, ` (a-c)/(b +c) =(c-a)/(d+a) " or, " (-(c-a))/(b+c) = (c-a)/(d+a)`
or, `(-(c-a))/(b+c) - (c-a)/(d+a) = 0 " or, " -(c-a) (1/(b+c) + 1/(d+a)) = 0`
or, ` - (c-a) {(d+a+b +c)/((b+c)(d+a))} = 0 " or, " -(c-a) {(a+b+c+d)/((b+c)(d+a))}= 0`
` :. " either " c - a = 0 " or, " (a +b + c+d)/((b+c)(d+a)) = 0`
`rArr c = a " or, " a + b + c + d = 0`
` :. " either " c = a " or, " a + b + c + d = 0`.