Get a common denominator which you can get by mutiplying by k-1
[tex] \frac{(k + 5)(k - 1)}{(k + 1)(k - 1)} + \frac{8}{ {k}^{2} - 1} [/tex]
Now foil and distribute
[tex] \frac{ {k}^{2} + 4k - 5}{ {k}^{2} - 1} + \frac{8}{ {k}^{2} - 1 } [/tex]
Now combine the fractions and like terms
[tex] \frac{ {k}^{2} + 4k - 5 + 8}{ {k}^{2} - 1 } = \frac{ {k}^{2} + 4k + 3}{ {k}^{2} - 1 } [/tex]
Now factor out a k+1
[tex] \frac{(k + 1)(k + 3)}{(k + 1)(k - 1)} [/tex]
you can cancel out the k+1 leaving
[tex] \frac{k + 3}{k - 1} [/tex]
