#### Answer

$ = \frac{(k+5)(k-7)}{(k+7)(k+3)}$

#### Work Step by Step

$\frac{k^{2}+k-20}{k^{2}+10k+21} \div \frac{k^{2}-10k+24}{k^{2}-13k+42}$
$ = \frac{k^{2}+k-20}{k^{2}+10k+21} \times \frac{k^{2}-13k+42}{k^{2}-10k+24}$
$ = \frac{(k-4)(k+5)}{(k+7)(k+3)} \times \frac{(k-6)(k-7)}{(k-6)(k-4)}$
$ = \frac{(k-4)(k+5)}{(k+7)(k+3)} \times \frac{(k-7)}{(k-4)}$
$ = \frac{(k+5)}{(k+7)(k+3)} \times \frac{(k-7)}{1}$
$ = \frac{(k+5)(k-7)}{(k+7)(k+3)}$