I'm trying to simplify the following expression $$\frac{n.r \ p.q - (n.p + n.q) (p.r + q.r)}{(n.p + n.q)\ p.q}\to \frac{n.r}{n.p+p.q}-\frac{p.r+q.r}{p.q}$$
When I put it into Mathematica and use FullSimplify
nothing happens though. For me it would be "simpler" to express this as a sum of "small" fractions.
I've tried using Apart
but that also does nothing. Could anyone recommend a way for me to force Mathematica to simplify an expression like this?