What is the answer to k²+9k+14/k²+8k+7*k²-9k/k²-7k-18

Question

I just need an answer

Answer 1

k²+9k+14=(k+7)(k+2); k²+8k+7=(k+7)(k+1);

therefore (k²+9k+14)/(k²+8k+7)=(k+7)(k+2)/((k+7)(k+1))=(k+2)/(k+1).

k²-9k=k(k-9); k²-7k-18=(k-9)(k+2); 

therefore (k²-9k)/(k²-7k-18)=k(k-9)/((k-9)(k+2))=k/(k+2).

So, [(k+2)/(k+1)]×[k/(k+2)]=k/(k+1).