Find g(f(x)) f(x)=3/(x-5) , g(x)=3/x+5

$f (x) = \frac{3}{x - 5}$ , $g (x) = \frac{3}{x} + 5$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (\frac{3}{x - 5})$ by substituting in the value of $f$ into $g$ .

$g (\frac{3}{x - 5}) = \frac{3}{\frac{3}{x - 5}} + 5$

Step 3

Simplify each term.

Multiply the numerator by the reciprocal of the denominator.

$g (\frac{3}{x - 5}) = 3 (\frac{x - 5}{3}) + 5$

Cancel the common factor of $3$ .

Cancel the common factor.

$g (\frac{3}{x - 5}) = 3 (\frac{x - 5}{3}) + 5$

Rewrite the expression.

$g (\frac{3}{x - 5}) = x - 5 + 5$

Step 4

Combine the opposite terms in $x - 5 + 5$ .

Add $- 5$ and $5$ .

$g (\frac{3}{x - 5}) = x + 0$

Add $x$ and $0$ .

$g (\frac{3}{x - 5}) = x$