No special name, just "combining fractions".

"All the different ways"? That could take a while!

Here's one:

Using the "associative law" combine the first two fractions: to subract

get a common denominator. Multiply both numerator and denominator of the first fraction by y+3 and of the second fraction by y+2:

Now the problem has become .

Again, get common denominators: multiply numerator and denominator of the first fraction by y-1 and of the second fraction by

You could, of course, multiply that denominator but I recommend leaving it factored.

By the associative law we could also combine the last two fractions, the add the first. Be careful to include the "-" sign with the second fractiononly. This is NOT

Or we could use the "commutative law swap the orders and combine in any order we please. Because of the associative law and commutative law, the order in which we add and subtract doesn't matter and most people would combine them "all at once", getting the common denominator by multiplying the numerator and denominator of the first fraction by (y+3)(y- 1), the second fraction by (y+2)(y-1), and the third fraction by (y+2)(y+3):