Simplify the expression P involving square roots and rational functions.

Let $a = \sqrt{2035}$. Then $a^2 = 2035$.
Let $b = \sqrt{2034}$. Then $b^2 = 2034$.
The expression for $P$ is:

$$P = \frac{\frac{a-1}{a+1} + \frac{a+3}{a-3} - \frac{b^2-b+7}{b^2-2b-2}}{b^2+3a+1}$$

Step 1: Simplify the sum of the first two terms in the numerator.

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