# Answer

m equals (5/3).

# Steps

((3m-5)/(m-3) ) plus (1/2)X 2(2m-3) equals (2m-3).

((3m-5)/(m-3)) plus (2m-3) equals (2m-3).

(2m-3) cancels out.

((3m-5)/(m-3)) equals 0.

It implies 3m-5 equals 0.

m equals 5/3.

m equals (5/3).

((3m-5)/(m-3) ) plus (1/2)X 2(2m-3) equals (2m-3).

((3m-5)/(m-3)) plus (2m-3) equals (2m-3).

(2m-3) cancels out.

((3m-5)/(m-3)) equals 0.

It implies 3m-5 equals 0.

m equals 5/3.