Hello there! My problem is probably really simple to solve however, I have managed to confused myself to a point of no return to I ask for whoever is on here to explain how to solve the equation found in the attached image. The equation is obtained from a Z-Transform control system time description along with a specific controller which gives a transfer function (equation 1). Once all the math-magic has been applied the transfer function will then be equation 2. My problem is I have no idea what steps are used to get equation 1 to equation 2. I assume partial fractions are used along with the Gaussian Elimination (which i really don't understand). Is it possible someone could show me the steps in detail as if i was an idiot? My math skills are beyond useless and I'm sure I have just missed something really simple.