Let a b c d Z with a c notequalto 0 Prove that if ab and cd

Let a, b, c, d Z with a, c notequalto 0. Prove that if a|b and c|d, then ac| (ad + bc).

Solution

if a/b then a =bk where k is some positive constant

c/d then c = dk ,

plugging in the value ,

bk*dk/(bkd +bdk)

=> bk.dk/ 2bd

=>k^2/2 hence a positive number ,

that means that ac/(ad+bc)