Solve the equation (3x+2)/(x-1)+3=4

First we must think about the fraction on the left hand side - we have to multiply everything by x-1 in order to get rid of the fraction. This leaves us with 3x+2+3(x-1)=4(x-1). Then, we must expand the brackets, which gives us 3x+2+3x-3=4x-4. Now we will collect similar terms, i.e. collect the xs together and the constants together, to get 6x-1=4x-4. Bringing all the x terms onto the left hand side, and the constant terms onto the right hand side, we get 2x=-3. Finally, dividing through by 2 we are left with x=-3/2, the solution to the equation.