Question

If S=P-3r and 1/p - 2/q=1/r.Express S in terms of q and r​

Answer 1

`S=(-2r(q+3r))/(q+2r)`

Explanation:

You are given two equalities
`S=p-3r` and
`(1)/(p)-(2)/(q)=(1)/(r)`

Express p from the second equality:

`(1)/(p)-(2)/(q)=(1)/(r)\\ \\(1)/(p)=(1)/(r)+(2)/(q)\\ \\(1)/(p)=(q+2r)/(rq)\\ \\(p)/(1)=p=(rq)/(q+2r)`

Substitute it into the first equality:

`S=(rq)/(q+2r)-3r=(rq-3r(q+2r))/(q+2r)=(rq-3rq-6r^2)/(q+2r)=(-2rq-6r^2)/(q+2r)=(-2r(q+3r))/(q+2r)`