(c) \( \frac{\frac{y}{x}-\frac{x}{y}}{\frac{6}{y}-\frac{6}{x}} \)

To simplify the expression \( \frac{\frac{y}{x}-\frac{x}{y}}{\frac{6}{y}-\frac{6}{x}} \), we can start by simplifying both the numerator and the denominator. The numerator can be rewritten as: \[ \frac{y}{x} - \frac{x}{y} = \frac{y^2 - x^2}{xy} = \frac{(y - x)(y + x)}{xy} \] For the denominator, we can factor out 6: \[ \frac{6}{y} - \frac{6}{x} = 6\left(\frac{1}{y} - \frac{1}{x}\right) = 6\left(\frac{x - y}{xy}\right) = \frac{6(x - y)}{xy} \] Now putting it all together, we have: \[ \frac{\frac{(y - x)(y + x)}{xy}}{\frac{6(x - y)}{xy}} = \frac{(y - x)(y + x)}{6(x - y)} \] Notice that \( y - x = -(x - y) \). Thus, we can rewrite the expression as: \[ \frac{-(x - y)(y + x)}{6(x - y)} = \frac{-(y + x)}{6} \] Therefore, the simplified expression is: \[ -\frac{y + x}{6} \]