I'm starting to work on this one question, but I'm not sure how to apply this inequality in it:

$\displaystyle \left|\left|z_1\right|-\left|z_2\right|\right|\leq\left|z_1+z_2\right|\le q\left|z_1\right|+\left|z_2\right|$

The question is : Find an upper bound for $\displaystyle \left|\frac{-4}{z^3-5z+1}\right|$ if $\displaystyle \left|z\right|=2$.

Now, I managed (in a previous question) to show that the lower and upper bounds on $\displaystyle \left|z^3-5z+1\right|$ when $\displaystyle \left|z\right|=2$ and I got $\displaystyle 3\leq\left|z^3-5z+1\right|\leq 19$....I have a feeling I need to incorporate this, but I'm not sure how.

Any input would be appreciated!!