(a + b) = (b + a)
(a - b) = -1x(b - a)
(a + b)² = (a² + 2ab + b²)
(a - b)² = (a² - 2ab + b²)
(a - b)x(a + b) = a² - b²

If you have a calculator, you might find it easy to turn fractions into float-point decimal values instead. For instance, if you have an equation that looks like 5/6x - 22x = 3, then you can always turn that into 0.83x - 22x = 3 (note: 0.8 is followed by an infinite number of 3's, so just put an overline on top of the 3 to indicate the float value repeats infinitely). So, just subtract 22x from that, and end up with -21.166666...X = 3. So divide both sides with -21.166666..., and get your happy results. Teachers don't seem to appreciate using tons of decimals, but if you can keep those "overlines", it's not faulty in any ways.

"Stephen Wolfram is the creator of Mathematica and is widely regarded as the most important innovator in scientific and technical computing today." - Stephen Wolfram