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A rational function can have a variable like "x" in the numerator AND the denominator. When this happens, there are some special rules and properties to consider.
Which of the following is the simplified expression of
\[ \frac{x^2 - 3x + 2}{x^2 - x - 6} \times \frac{x^2 - 4x + 3}{x^2 - 4}? \]
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Simplify
\[ \frac{1}{x (x+2)} + \frac{1}{(x+2) (x+4)} + \frac{1}{(x+4) (x+6)} + \frac{1}{(x+6) (x+8)}. \]
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Simplify
\[ 1 - \frac{1}{1 - \dfrac{1}{1-x}}. \]
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If real numbers \(x\) and \(y\) satisfy \( \frac{x^3+y^3}{x^3-y^3} = \frac{7}{9}, \) what is the value of \[ \frac{x+y}{x-y}?\]
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Which of the following is the simplified expression of
\[ \frac{2r}{r^2 - s^2} + \frac{1}{r+s} - \frac{1}{r-s} ? \]
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