Questions

Simplify: $\rm \frac{1}{a+1} + \frac{2}{1 + a^2} + \frac{4}{a^4 - 1}$

Simplify: $\rm \frac{2 (1 + c^4)}{1 - c^4} + \frac{4c^2}{1 + c^4} + \frac{8c^6}{1 - c^8}$

Simplify: $\rm \frac{1}{(x+1)^2 (x+2)^2} - \frac{1}{(x+1)^2} + \frac{2}{x+1} - \frac{2}{x+2}$

Simplify: $\rm \frac{2}{(y+1)(y+2)} + \frac{1}{(y+1)^2 (y+2)^2} - \frac{1}{(y+1)^2}$

Simplify: $\rm \left ( \frac{1}{a} + \frac{1}{b} \right ) \left ( a + b -c \right ) + \left ( \frac{1}{b} + \frac{1}{c} \right ) \left ( b + c -a \right ) + \left ( \frac{1}{c} + \frac{1}{a} \right ) \left ( c + a - b \right )$

Simplify: $\rm \frac{a+b}{2ab} \left ( a + b - c \right ) + \frac{b+c}{2bc} \left ( b + c - a \right ) + \frac{c+a}{2ca} \left ( c + a - b \right )$

Simplify: $\rm \frac{2}{1 - a^2} + \frac{2}{1 + a^2} + \frac{4}{1 + a^4}$

Simplify: $\rm \frac{x+3}{x^2 + 3x + 9} + \frac{x-3}{x^2 - 3x + 9} - \frac{54}{x^4 + 9x^2 + 81}$

Simplify: $\rm \frac{y-2}{y^2 - 2y + 4} + \frac{y+2}{y^2 + 2y + 4} - \frac{16}{y^4 + 4y^2 + 16}$

Simplify: $\rm \frac{a+2}{1 + a + a^2} - \frac{a-2}{1 - a + a^2} - \frac{2a^2}{1 + a^2 + a^4}$