For the given functions f(x) and g(x), find f(x) ÷ g(x).
-$$f ( x ) = ( x - 6 ) , g ( x ) = \frac { 2 x ^ { 2 } - 6 x - 36 } { x ^ { 2 } - 9 x + 18 }$$
A) $\frac { x - 3 } { 2 x + 6 }$

B) $\frac { ( x - 6 ) ( x - 3 ) } { 2 x + 6 }$

C) $\frac { ( x - 6 ) ^ { 2 } ( x - 3 ) } { 2 x + 6 }$

D) $\frac { ( x + 6 ) ( x - 3 ) } { 2 x - 6 }$

Question

For the given functions f(x) and g(x), find f(x) ÷ g(x).
-$$f ( x ) = ( x - 6 ) , g ( x ) = \frac { 2 x ^ { 2 } - 6 x - 36 } { x ^ { 2 } - 9 x + 18 }$$
A) $\frac { x - 3 } { 2 x + 6 }$

B) $\frac { ( x - 6 ) ( x - 3 ) } { 2 x + 6 }$

C) $\frac { ( x - 6 ) ^ { 2 } ( x - 3 ) } { 2 x + 6 }$

D) $\frac { ( x + 6 ) ( x - 3 ) } { 2 x - 6 }$

Quizplus · Accepted Answer

To divide two functions, we must multiply the first function by the reciprocal of the second function. Therefore, we have:
$$\frac {f(x)}{g(x)} = f(x) \cdot \frac{1}{g(x)}$$
$$f(x) \cdot \frac{1}{g(x)} = f(x) \cdot \frac{x^{2}-9x+18}{2x^{2}-6x-36}$$
$$f(x) \cdot \frac{x^{2}-9x+18}{2x^{2}-6x-36} = (x-6) \cdot \frac{x^{2}-9x+18}{2(x^{2}-3x-18)}$$
$$= (x-6) \cdot \frac{(x-3)(x-6)}{2(x-6)(x+3)}$$
$$= \frac{(x-6)(x-3)}{2(x+3)}$$
Therefore, the answer is B.

For the Given Functions F(x) and G(x), Find F(x) ÷ f(x)=(x−6),g(x)=2x2−6x−36x2−9x+18f ( x ) = ( x - 6 ) , g ( x ) = \frac { 2 x ^ { 2 } - 6 x - 36 } { x ^ { 2 } - 9 x + 18 }f(x)=(x−6),g(x)=x2−9x+182x2−6x−36​

For the Given Functions F(x) and G(x), Find F(x) ÷ $f ( x ) = ( x - 6 ) , g ( x ) = \frac { 2 x ^ { 2 } - 6 x - 36 } { x ^ { 2 } - 9 x + 18 }$