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

The equation looks horrible to start so we need to tidy it up. We do this by firstly getting rid of the fraction. This means that we need to multiply everything else by the denominator (which in this case is x-1). By multiplying the top fraction (the numerator) the denominator disappears to leave the top (3x+2), we then multiply 3 by x-1, remembering to leave x-1 in the bracket so that we multiply both the x and the -1 by the 3, which gives us 3x-3 (remember the minus), as 3 multiplied by x gives us 3x, and 3 multiplied by -1 gives us -3. Lastly we multiply the other side by the denominator (4 x x-1) so 4 multiplied by x= 4x and 4 multiplied by -1 gives us -4. This means the equation becomes 3x+2 +3x-3= 4x-4. As there are two lots of 3x (one variable) we need to simplify it so we add 3x to 3x to get 6x, and we add 2 to -3 to make the equation simpler, 2-3= -1. This means we now have 6x-1=4x-4. We want to get x's on one side and numbers on the other, so we usually use the smallest number of x's (in this case 4x) and minus 4x from that side (as we have a positive x we minus this to the other side). 6x therefore becomes 2x as we have taken 4x from it, this becomes 2x-1= -4. We want to get the -1 on the opposite side, and because it is a minus we add it to the other side. This means the -1 disappears from the left hand side (as -1 +1 =0) and on the right hand side -4+1 becomes -3. Hence the equation looks much neater and is 2x=-3. We are told to solve the equation which means we want to find x and so we need x on its own and not 2x. As 2 is multiplied by x we need to divide x by 2 (doing the opposite) and so we divide both sides by 2, 2x/2=x and -3 divided by 2=-3/2. This leaves us with x= -3/2!