simplify (2q+4)/(p(p+1)) -q/p

times the whole equation by the denominator of the left fraction giving p(2q+4)(p+1) - (qp(p+1))/p

notice that p can be cancelled in the right fraction, and then times out to give

2qp^2 + 4p + 4p^2 + 2pq - qp + q

This can be factorised in this way

p(2p(q+4)+(q+4))+q

and then further

p(q+4)(2p+1)+q