Divide as indicated.
-$$\frac { x ^ { 2 } + 16 x + 64 } { x ^ { 2 } + 17 x + 72 } \div \frac { x ^ { 2 } + 8 x } { x ^ { 2 } + 3 x - 54 }$$
A) $\frac { x } { x ^ { 2 } + 17 x + 72 }$
B) $\frac { x - 6 } { x ^ { 2 } + 9 x }$
C) $\frac { x - 6 } { x }$
D) $x - 6$

Question

Quizplus · Accepted Answer

First, factorize all the quadratic expressions:- $x^2 + 16x + 64 = (x + 8)^2$- $x^2 + 17x + 72 = (x + 8)(x + 9)$- $x^2 + 8x = x(x + 8)$- $x^2 + 3x - 54 = (x + 9)(x - 6)$The division can be rewritten as multiplication by the reciprocal:$$\frac{(x + 8)^2}{(x + 8)(x + 9)} \times \frac{(x + 9)(x - 6)}{x(x + 8)}$$Simplify by canceling out common factors:$$\frac{(x + 8)(x - 6)}{x}$$This simplifies to:$$\frac{x - 6}{x}$$

Divide as Indicated x2+16x+64x2+17x+72÷x2+8xx2+3x−54\frac { x ^ { 2 } + 16 x + 64 } { x ^ { 2 } + 17 x + 72 } \div \frac { x ^ { 2 } + 8 x } { x ^ { 2 } + 3 x - 54 }x2+17x+72x2+16x+64​÷x2+3x−54x2+8x​

Divide as Indicated $\frac { x ^ { 2 } + 16 x + 64 } { x ^ { 2 } + 17 x + 72 } \div \frac { x ^ { 2 } + 8 x } { x ^ { 2 } + 3 x - 54 }$