multiply and simplify
k^2+10k+16 k^2+6k
__________ x _________
k^2+14k+48 k^2+5k+6
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)
To multiply and simplify the given expression:
Step 1: Factor both the numerator and the denominator of each fraction.
k^2 + 10k + 16 = (k + 8)(k + 2)
k^2 + 14k + 48 = (k + 6)(k + 8)
k^2 + 6k = k(k + 6)
k^2 + 5k + 6 = (k + 3)(k + 2)
Step 2: Combine the fractions by multiplying the numerators together and the denominators together.
[(k + 8)(k + 2) / (k + 6)(k + 8)] x [k(k + 6) / (k + 3)(k + 2)]
Step 3: Cancel out the common factors between the numerator and the denominator.
[(k + 8) * cancel(k + 2) / cancel(k + 6) * cancel(k + 8)] x [k * cancel(k + 6) / (k + 3) * cancel(k + 2)]
Step 4: Simplify the expression.
= k / (k + 3)
Therefore, the multiplied and simplified expression is k / (k + 3).