His this is an example problem from hall and knight's higher algebra book,

it says

if $\displaystyle x/l(mb+nc-la) = y/m(nc+la-mb) = z/n(la+mb-nc$)

then prove that

$\displaystyle l/x(by+cz-ax) = m/y(cz+ax-by) = n/z(ax+by-cz)$

can you please tell me the steps one should go through to prove this?