p + r = mq and 1/q+ 1/s = m/r prove p:q = r:s
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r+q/qr=m/r
qrm=R(r+q)
qrm=r²+rq
r²+rq-rqm=0
r(r+q-qm)=0
r=0 or .r+q(1-m)=0
r= -q(1-m)
-q(1-m)=0
1-m=0
m=1
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