how to solve the sampling rate conversion problem

I am trying to improve my DSP knowledge and this problem is too much for me. I am trying to solve following task:
this is not a homework. any help will be appreciated.

• Which book it is from? Take the frequency domain approach to solve this.. – Oliver Apr 20 '15 at 2:53
• Equations are fairly straightforward. Your filter gain should be equal to $L$, cutoff frequency is always defined as $\omega/L$ and re-sampled frequency is $f_2=f_1\cdot L/M$. – jojek Apr 20 '15 at 22:37
• @jojek: will you be post comment as the answer? i can accept it – Black Yasmin Mar 16 '16 at 8:48