Given p/q = 5/6, q/r = 7/10, and r/s = 9/4, find
(p - q)/(q - r) and (2q - r)/(r + s)
p/q = 5/6, q/r = 7/10, and r/s = 9/4
q = (6/5)p
q/r = 7/10
(6/5)p / r = 7/10
r = (6/5)p (10/7) = (60/35)p = ( 12/7)p
r/s = 9/4
(12/7)p / s = 9/4
s = (12/7)p ( 4/9) = (48/63)p = ( 16/21)p
So
(p - q) / (q - r) = (p - 6/5)p) / ( 6/5 p - 12/7 p) = (1/5 p ) / (-18/37 p ) = (1/5) ( -37/18) = -37/90
And
(2q - r) / (r + s) = [ (12/5)p - (12/7) p] / (12/7 p + 16/21 p) = (24/35 p) / (52/21 p) =
(24/35) (21/52) = (24/52) ( 21/35) = (6/13) (3/5) = 18/65