x is a negative number such that k + k^-1 = -2, then what is the value of $$\frac{{{k^2} + 4k - 2}}{{{k^2} + k - 5}}?$$

$$\eqalign{ & k + \frac{1}{k} = 2 \cr & k = - 1 \cr & \frac{{{k^2} + 4k - 2}}{{{k^2} + k - 5}} \cr & = \frac{{{{\left( { - 1} \right)}^2} + 4\left( { - 1} \right) - 2}}{{{{\left( { - 1} \right)}^2} + \left( { - 1} \right) - 5}} \cr & = \frac{{1 - 4 - 2}}{{1 - 1 - 5}} \cr & = \frac{{ - 5}}{{ - 5}} \cr & = 1 \cr} $$