For the given functions f(x) and g(x), find f(x) ÷ g(x).
-$$f ( x ) = \frac { x ^ { 2 } - 11 x + 30 } { x ^ { 2 } - 8 x + 15 } , g ( x ) = \left( x ^ { 2 } - 9 x + 18 \right)$$
A) $( x + 3 ) ^ { 2 }$

B) $\frac { 1 } { ( x + 3 ) ^ { 2 } }$

C) $( x - 6 ) ^ { 2 }$

D) $\frac { 1 } { ( x - 3 ) ^ { 2 } }$

Question

For the given functions f(x) and g(x), find f(x) ÷ g(x).
-$$f ( x ) = \frac { x ^ { 2 } - 11 x + 30 } { x ^ { 2 } - 8 x + 15 } , g ( x ) = \left( x ^ { 2 } - 9 x + 18 \right)$$
A) $( x + 3 ) ^ { 2 }$

B) $\frac { 1 } { ( x + 3 ) ^ { 2 } }$

C) $( x - 6 ) ^ { 2 }$

D) $\frac { 1 } { ( x - 3 ) ^ { 2 } }$

Quizplus · Accepted Answer

To divide two functions, we need to multiply the first function by the reciprocal of the second function.
$$f(x)÷g(x)=f(x)\times \frac{1}{g(x)}= \frac{x^2-11x+30}{x^2-8x+15}\times\frac{1}{x^2-9x+18}$$
Factor the denominators of both terms.
$$\frac{(x-6)(x-5)}{(x-5)(x-3)} \times \frac{1}{(x-6)(x-3)}$$
Cancel out the common factors and simplify.
$$\frac{1}{(x-3)^2}$$
Therefore, the answer is D, $\frac{1}{(x-3)^2}$.

For the Given Functions F(x) and G(x), Find F(x) ÷ f(x)=x2−11x+30x2−8x+15,g(x)=(x2−9x+18)f ( x ) = \frac { x ^ { 2 } - 11 x + 30 } { x ^ { 2 } - 8 x + 15 } , g ( x ) = \left( x ^ { 2 } - 9 x + 18 \right)f(x)=x2−8x+15x2−11x+30​,g(x)=(x2−9x+18)

For the Given Functions F(x) and G(x), Find F(x) ÷ $f ( x ) = \frac { x ^ { 2 } - 11 x + 30 } { x ^ { 2 } - 8 x + 15 } , g ( x ) = \left( x ^ { 2 } - 9 x + 18 \right)$