Find the product or quotient.
-$$\frac { k ^ { 2 } + 11 k + 30 } { k ^ { 2 } + 12 k + 36 } \cdot \frac { k ^ { 2 } + 6 k } { k ^ { 2 } - 4 k - 45 }$$

A) $\frac { k } { k ^ { 2 } + 12 k + 36 }$

B) $\frac { k } { k - 9 }$

C) $\frac { 1 } { k - 9 }$

D) $\frac { k ^ { 2 } + 6 k } { k - 9 }$

Question

Find the product or quotient.
-$$\frac { k ^ { 2 } + 11 k + 30 } { k ^ { 2 } + 12 k + 36 } \cdot \frac { k ^ { 2 } + 6 k } { k ^ { 2 } - 4 k - 45 }$$

A) $\frac { k } { k ^ { 2 } + 12 k + 36 }$

B) $\frac { k } { k - 9 }$

C) $\frac { 1 } { k - 9 }$

D) $\frac { k ^ { 2 } + 6 k } { k - 9 }$

Quizplus · Accepted Answer

First, factor each polynomial:- $k^2 + 11k + 30 = (k + 5)(k + 6)$- $k^2 + 12k + 36 = (k + 6)^2$- $k^2 + 6k = k(k + 6)$- $k^2 - 4k - 45 = (k - 9)(k + 5)$Substitute the factored forms into the original expression:$$\frac{(k + 5)(k + 6)}{(k + 6)^2} \cdot \frac{k(k + 6)}{(k - 9)(k + 5)}$$Cancel out common factors:- The $(k + 5)$ terms cancel out.- One $(k + 6)$ term cancels out from the numerator and denominator.This leaves:$$\frac{k}{k - 9}$$Therefore, the correct answer is B.

Find the Product or Quotient k2+11k+30k2+12k+36⋅k2+6kk2−4k−45\frac { k ^ { 2 } + 11 k + 30 } { k ^ { 2 } + 12 k + 36 } \cdot \frac { k ^ { 2 } + 6 k } { k ^ { 2 } - 4 k - 45 }k2+12k+36k2+11k+30​⋅k2−4k−45k2+6k​

Find the Product or Quotient $\frac { k ^ { 2 } + 11 k + 30 } { k ^ { 2 } + 12 k + 36 } \cdot \frac { k ^ { 2 } + 6 k } { k ^ { 2 } - 4 k - 45 }$