For the given functions f(x) and g(x), find f(x) ∙ g(x).
-$$f ( x ) = \frac { x ^ { 2 } - 9 x + 18 } { x ^ { 2 } - 7 x + 12 } , g ( x ) = \frac { x ^ { 2 } + 3 x - 4 } { x ^ { 2 } - 7 x + 6 }$$
A) 1
B) $\frac { x - 4 } { x + 4 }$

C) $\frac { x + 4 } { x - 4 }$
D) $- 1$

Question

For the given functions f(x) and g(x), find f(x) ∙ g(x).
-$$f ( x ) = \frac { x ^ { 2 } - 9 x + 18 } { x ^ { 2 } - 7 x + 12 } , g ( x ) = \frac { x ^ { 2 } + 3 x - 4 } { x ^ { 2 } - 7 x + 6 }$$
A) 1
B) $\frac { x - 4 } { x + 4 }$

C) $\frac { x + 4 } { x - 4 }$
D) $- 1$

Quizplus · Accepted Answer

To find the product, we just need to multiply the two fractions: 
$$f(x) \cdot g(x) = \frac{x^2-9x+18}{x^2-7x+12} \cdot \frac{x^2+3x-4}{x^2-7x+6}$$
We can factor the denominators and simplify:
$$f(x) \cdot g(x) = \frac{(x-3)(x-6)}{(x-4)(x-3)} \cdot \frac{(x+4)(x-1)}{(x-6)(x-1)}$$
Cancel out the common factors:
$$f(x) \cdot g(x) = \frac{(x-3)(x+4)}{(x-4)}$$
$$f(x) \cdot g(x) = \frac{x^2+x-12}{x-4}$$
We can further simplify:
$$f(x) \cdot g(x) = \frac{(x-4)(x+3)}{x-4}$$
$$f(x) \cdot g(x) = x+3$$
Therefore, the answer is C, $\frac{x+4}{x-4}$

For the Given Functions F(x) and G(x), Find F(x) ∙ f(x)=x2−9x+18x2−7x+12,g(x)=x2+3x−4x2−7x+6f ( x ) = \frac { x ^ { 2 } - 9 x + 18 } { x ^ { 2 } - 7 x + 12 } , g ( x ) = \frac { x ^ { 2 } + 3 x - 4 } { x ^ { 2 } - 7 x + 6 }f(x)=x2−7x+12x2−9x+18​,g(x)=x2−7x+6x2+3x−4​

For the Given Functions F(x) and G(x), Find F(x) ∙ $f ( x ) = \frac { x ^ { 2 } - 9 x + 18 } { x ^ { 2 } - 7 x + 12 } , g ( x ) = \frac { x ^ { 2 } + 3 x - 4 } { x ^ { 2 } - 7 x + 6 }$