\( 1 - \frac {a - b \cdot \frac {a - b}{a + b}}{b - a \cdot \frac {a + b}{a - b}} =\answer [onlineshowanswerbutton]{\frac {2a}{a + b} } \)
\( \frac {\left ( - \left ( x + \frac {a^2}{x + a} \right ) \left ( a + \frac {x^2}{a - x} \right ) \right )}{x^6 - a^6} \cdot (x^2 - a^2)^2 =\answer [onlineshowanswerbutton]{1 } \)
\( \frac {a}{a^2 - b^2} + \frac {a^2 - ab + b^2}{b^3 - a^3} - \frac {b}{(a + b)^2} =\answer [onlineshowanswerbutton]{\frac {2a^2 b^2}{(a - b)(a + b)^2 (a^2 + ab + b^2)} } \)
\( \frac {a^2 + ab + b^2}{a^3 + b^3} + \frac {a^2 - ab + b^2}{a^3 - b^3} + \frac {4ab^4}{a^6 - b^6} =\answer [onlineshowanswerbutton]{\frac {2a}{a^2 - b^2} } \)
\( \left ( x + \frac {1}{x^2} + 3 \left ( 1 + \frac {1}{x} \right ) \right ) : \left ( \frac {1}{x} \left ( 1 + \frac {1}{x} \right )^2 \right ) =\answer [onlineshowanswerbutton]{x(x + 1) } \)
\( \frac {\frac {a + b}{a - b} + \frac {a - b}{a + b} + 2}{\frac {a + b}{a - b} + \frac {a - b}{a + b} - 2} : \frac {\frac {a + 2b}{a - 2b} + \frac {a - 2b}{a + 2b} + 2}{\frac {a + 2b}{a - 2b} + \frac {a - 2b}{a + 2b} - 2} =\answer [onlineshowanswerbutton]{4 } \)