For the given rational functions f(x) and g(x), f(x) +g(x).
-$$f ( x ) = \frac { 7 x + 4 } { 7 x + 9 } , g ( x ) = \frac { 7 x + 14 } { 7 x + 9 }$$
A) $\frac { 8 x + 10 } { 7 x + 9 }$
B) $\frac { 2 } { 7 x + 9 }$
C) 2
D) 1

Question

Quizplus · Accepted Answer

To find $f(x) + g(x)$, we add the two given functions together. Since they have the same denominator, we can combine the numerators directly:$$f(x) + g(x) = \frac{7x + 4}{7x + 9} + \frac{7x + 14}{7x + 9} = \frac{(7x + 4) + (7x + 14)}{7x + 9} = \frac{14x + 18}{7x + 9}$$Simplifying the numerator:$$14x + 18 = 2(7x + 9)$$So, when we place this over the common denominator $7x + 9$, we get:$$\frac{2(7x + 9)}{7x + 9} = 2$$Therefore, the correct answer is 2, which corresponds to choice C.

For the Given Rational Functions F(x) and G(x), F(x) +G(x) f(x)=7x+47x+9,g(x)=7x+147x+9f ( x ) = \frac { 7 x + 4 } { 7 x + 9 } , g ( x ) = \frac { 7 x + 14 } { 7 x + 9 }f(x)=7x+97x+4​,g(x)=7x+97x+14​

For the Given Rational Functions F(x) and G(x), F(x) +G(x) $f ( x ) = \frac { 7 x + 4 } { 7 x + 9 } , g ( x ) = \frac { 7 x + 14 } { 7 x + 9 }$