Apart

Apart(expr)

rewrites expr as a sum of individual fractions.

Apart(expr, var)

treats var as main variable.

>> Apart((x-1)/(x^2+x))
2/(x+1)-1/x

>> Apart(1 / (x^2 + 5x + 6))
1/(2+x)+1/(-3-x)

When several variables are involved, the results can be different depending on the main variable:

>> Apart(1 / (x^2 - y^2), x)
-1 / (2 y (x + y)) + 1 / (2 y (x - y))

>> Apart(1 / (x^2 - y^2), y)
1 / (2 x (x + y)) + 1 / (2 x (x - y))

Apart is Listable:

>> Apart({1 / (x^2 + 5x + 6)})
{1/(2+x)+1/(-3-x)}

But it does not touch other expressions:

>> Sin(1 / (x ^ 2 - y ^ 2)) // Apart
Sin(1/(x^2-y^2))