multiply and simplify

Question

k^2+10k+16 k^2+6k
__________ x _________
k^2+14k+48 k^2+5k+6

Answer 1

I assume that is supposed to represent two fractions which are to be multiplied.

k^2 + 10k + 16 = (k+8)(k+2)
k^2 + 1k + 48 = (k+8)(k+6)

So, the first fraction reduces to
(k+2)/(k+6)

k^2 + 6k = k(k+6)
k^2 + 5k + 6 = (k+2)(k+3)

So, multiplying, we have

(k+2)(k)(k+6) / (k+6)(k+2)(k+3)

= k/(k+3)