Add .

This time around, our common denominator (LCM) is (a + 1)(a + 2). Multiply each term by the appropriate ratio of 1 so they're both in LCM mode.

Simplify the numerator and put everything over the LCM.

Now we just combine like terms in the numerator.

Subtract .

Factor the denominators so you can find the LCM.

All right, we've got one copy of (x – 1) in each fraction, so we'll take that to the first power. The highest power of the other factors, (x + 2) and (x + 3), is also just 1, so our LCM is (x – 1)(x + 2)(x + 3).

So multiply each term by an appropriate ratio of 1 to get them both over the LCM.

Now multiply out the numerator.

Remove the parentheses and collect like terms in the numerator, like a stamp fiend collects stamps.

Simplify into a single fraction.

The denominator d ² – 1 factors to (d + 1)(d – 1). So (d + 1)(d – 1) is the LCM.

Multiply the other two terms by an appropriate ratio of 1 to get them all over the LCM.

Now multiply out the numerator.

Wrap this bad boy up by collecting like terms in the numerator.