Answer
$f’(x) = \frac{6}{(x+2)^{2}}$
$g’(x) = \frac{6}{(x+2)^{2}}$
The slope of f(x) is equal to the slope of g(x). They are parallel fucntions.
Work Step by Step
Quotient rule: $\frac{d}{dx}$$\frac{f(x)}{g(x)}$ = $\frac{g(x)f’(x)-f(x)g’(x)}{g(x)g(x)}$
$f(x) = \frac{3x}{x+2}$
$f’(x) = \frac{(x+2)(3)-(3x)(1)}{(x+2)^{2}}$ = $\frac{3x+6-3x}{(x+2)^{2}}$ = $\frac{6}{(x+2)^{2}}$
$g(x) = \frac{5x+4}{x+2}$
$g’(x) = \frac{(x+2)(5)-(5x+4)(1)}{(x+2)^{2}}$=$\frac{5x-10-5x-4}{(x+2)^{2}}$=$\frac{6}{(x+2)^{2}}$
