For a sample word problem I'm looking at, after you determine the equation, you have to solve it. This is the first step... finding the common denominator

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I'm okay with it past that step, the answer then is 30(x+1) - 30x = x^2 + x which I have no clue how to get...

After that, it's just 30x + 30 - 30x = x^2 + x, then 30 = x^2 + x, 0 = x^2 + x -30, 0 = (x+6)(x-5), x+6=0 and x-5=0, x=-6, x=5 which is okay but the first part just confuses me so much, I have no clue how any of that works - I know obviously what a common denominator is but I have no clue what happened to any number on that fraction to make it turn into what it became... unfortunately since this is the first step on several problems (including problems that end up being in the ax^2+bx+c quadratic form), and I understand the parts after it (simple solving or finding the roots from the quadratic equation) but this I have no idea how to do...