Question 43703
You have a good start to the problem however remember the idea is to remove denominators 

x+1/2x+3 = 2/3  Remember if a/b=c/d the ac=bd  We have
3(x+1)=2(2x+3)
3x+3=4x+6
-3 =x
When you plug -3 into the origianal equation you will get -2/-3 which is equivalent