Question 176318
The claim is false. Here's a counter-example to show why:


Let d=10, a=3, and b=7 (you can pick any random numbers as long as d does not divide either a or b, but it divides the sum)


It is true that d does NOT divide a (since 10 does NOT divide 3) and d does NOT divide b (since 10 does NOT divide 7). 


However, d does divide a+b since 10 divides (3+7) or 10. In other words, {{{10/(3+7)=10/10=1}}}