Rearrange y=(3x+5)/x to make x the subject

This question is asking us to make x the subject, so we’re aiming to end up with just x on its own on one side of the equation. Firstly, we need to get rid of the x on the bottom of the right-hand side, so to do this we can multiply both sides by x, and because multiplication is the opposite of division, this will cancel out that x, making the equation xy=3x+5. Now remember we want to get all of the x’s on one side, so next we will subtract 3x from both sides (cancelling out the 3x on the right-hand side as subtraction is the opposite of addition) leaving us with xy-3x=5. We now have all the x’s on the left-hand side so that’s the hard bit done! Now we can look at the left hand side and see that all of the terms have an x in, so we can factorise this out, giving us x(y-3)=5. We want just the x on its own, so we can divide both sides by (y-3), which leaves us with x=5/(y-3). As you can see, we now have x on the left-hand side with everything else on the right, meaning that it is now the subject of the equation!