Prove sum of 2 little 'o is equal to the little 'o from the sum

Question

I need to prove if

for $f(x) = o(h(x))$ and $g(x) = o(q(x))$

then $f(x) + g(x) = o(|h(x)| + |q(x)|)$

I think that this is false but I am struggling to find a counter example.

Answer 1

Hint: if $|f(x)| \le a |h(x)|$ and $|g(x)| \le a |q(x)|$ then $|f(x) + g(x)| \le a (|h(x)| + |q(x)|)$.