Given equality:
#\frac{3x}{x-5}=5-\frac{5}{x-5}=15#
#\frac{3x}{x-5}=\frac{5x-30}{x-5}=15#
1) Consider
#\frac{3x}{x-5}=\frac{5x-30}{x-5}#
#\frac{3x}{x-5}-\frac{5x-30}{x-5}=0#
#\frac{3x-5x+30}{x-5}=0#
#\frac{-2x+30}{x-5}=0#
#-2x+30=0\ \quad (\forall \ x\ne 5)#
#2x=30#
#x=15#
2) Consider
#\frac{3x}{x-5}=15#
#x=5(x-5)#
#4x=25#
#x=25/4#
#x=6.25#
3) Consider
#\frac{5x-30}{x-5}=15#
#5x-30=15(x-5)#
#10x=45#
#x=4.5#
Since, the values of #x# in all three cases are different hence the given equality doesn't have any solution
