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

Question

Quizplus · Accepted Answer

To add the two rational functions, we need to find the common denominator. In this case, the denominator of both functions is the same. So, we add the two numerators and put them over the common denominator.
$$f(x)+g(x)=\frac{x^2-7x+6x-12}{x^2+6x+9}=\frac{x^2-x-12}{(x+3)^2}$$
Now, we factor the numerator:
$$\frac{(x-4)(x+3)}{(x+3)^2}=\frac{x-4}{x+3}$$
Therefore, the correct choice is B.

For the Given Rational Functions F(x) and G(x), F(x) +G(x) f(x)=x2−7xx2+6x+9,g(x)=6x−12x2+6x+9f ( x ) = \frac { x ^ { 2 } - 7 x } { x ^ { 2 } + 6 x + 9 } , g ( x ) = \frac { 6 x - 12 } { x ^ { 2 } + 6 x + 9 }f(x)=x2+6x+9x2−7x​,g(x)=x2+6x+96x−12​

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