Prove or Disprove: for All Integers $$a , b , c , d \text {, if } a \mid b \text { and } c \mid d \text {, then } ( a c ) \mid ( b + d ) \text {. }$$

Prove or disprove: For all integers $$a , b , c , d \text {, if } a \mid b \text { and } c \mid d \text {, then } ( a c ) \mid ( b + d ) \text {. }$$