Find g(f(x)) f(x)=(6+x)/(x-4) , g(x)=3/x

$f (x) = \frac{6 + x}{x - 4}$ , $g (x) = \frac{3}{x}$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (\frac{6 + x}{x - 4})$ by substituting in the value of $f$ into $g$ .

$g (\frac{6 + x}{x - 4}) = \frac{3}{\frac{6 + x}{x - 4}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$g (\frac{6 + x}{x - 4}) = 3 (\frac{x - 4}{6 + x})$

Step 4

Combine $3$ and $\frac{x - 4}{6 + x}$ .

$g (\frac{6 + x}{x - 4}) = \frac{3 (x - 4)}{6 + x}$