Question

The ratio (m-2c) : (m+c) is equivalent to 1 : k show that m= c(2k+1)/k-1

Answer 1

$\bf m-2c~:~m+c~~=~~1:k\qquad \implies \cfrac{m-2c}{m+c}=\cfrac{1}{k}\implies k(m-2c)=m+c \\\\\\ mk-2kc=m+c\implies mk-m-2kc=c\implies mk-m=2kc+c \\\\\\ \stackrel{\textit{common factor}}{m(k-1)=c(2k+1)}\implies m=\cfrac{c(2k+1)}{k-1}$