Proving an upper bound to F(x)+G(x)

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I have stumbled upon the following question: If $f(x),g(x) > 1$ for every $x$, prove/disprove the following:

$$f(x)+g(x)= O\left(f(x)g(x)\right)$$

I dont know how to start the proof, this is very basic for my level, please help.

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Hint: Write down the definition of the Landau notation and then use the triangular inequality.