Now on the second part, it is finding the equation of ax +by = 1, which i am generally having to find so i can compute the inverse of a(modb). They have managed to do this in 7 steps. It always takes me like more than twice as many in a really longwinded fashion. Has the example below missed out some steps for the sake of conciseness? I just dont understand how they are doing what they are doing.

For example I would have said

1= 3- 2

1 = (20-17) - (17 - (5x3))

1 = ((57-37) - (37-20)) - ((37-20) - 5(20-17))

etc.

Which is obviously far more longwinded, but equally as methodical. I want to know how to do this more concisely so in an exam it would be far less confusing and time consuming.