Answer to Question #6282 in Abstract Algebra for Nguyen

Question

1/2m-3=5/6-2/3m

Answer 1

1/(2m-3)=5/6-2/3m
1/(2m-3)+2/3m=5/6
(3m+4m-6)/(3m*(2m-3))=5/6
Note that m<>3/2 and m<>0
42m-36=15m(2m-3)=30m^2-45m
30m^2-87m+36=0
D=87^2-4*30*36=57^2
m1=(87+57)/60=144/60=72/30=36/15=12/5
m2=(87-57)/60=1/2