Simplify the following algebraic fractions.
$A) \frac{1}{a} + \frac{2}{a + 2} (B) \frac{t - 1}{t + 1} + \frac{1}{t^{2} - 1}$

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Solution

$A) \frac{1}{a} + \frac{2}{a + 2} \frac{1}{x + 1} + \frac{2}{x + 2} \frac{5}{4 x + 1} - \frac{1}{3 (2 x + 1)} \frac{2}{x + 5} + \frac{3}{x - 2} + \frac{1}{x} \frac{3}{2 (y - 2)} + \frac{2}{3 (y - 2)} \frac{4}{3 (x + 1)} - \frac{2}{5 (x - 1)}$
$B) \frac{t - 1}{t + 1} + \frac{1}{t^{2} - 1} \frac{1}{a - 3} + \frac{1}{a^{2} - a - 6} \frac{1}{x^{2} + 4 x + 4} - \frac{1}{(x - 2) (x + 2)} \frac{1}{2 a + 1} + \frac{1}{a^{2} + 3 a + 2}$

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