Find the Product f(x)=x/(x-2) , g(x)=(3x)/(x+4)

$f (x) = \frac{x}{x - 2}$ , $g (x) = \frac{3 x}{x + 4}$

Step 1

Replace the function designators with the actual functions in $f (x) \cdot (g (x))$ .

$(\frac{x}{x - 2}) \cdot (\frac{3 x}{x + 4})$

Step 2

Multiply $(\frac{x}{x - 2}) (\frac{3 x}{x + 4})$ .

Multiply $\frac{x}{x - 2}$ by $\frac{3 x}{x + 4}$ .

$\frac{x (3 x)}{(x - 2) (x + 4)}$

Raise $x$ to the power of $1$ .

$\frac{3 (x^{1} x)}{(x - 2) (x + 4)}$

Raise $x$ to the power of $1$ .

$\frac{3 (x^{1} x^{1})}{(x - 2) (x + 4)}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{3 x^{1 + 1}}{(x - 2) (x + 4)}$

Add $1$ and $1$ .

$\frac{3 x^{2}}{(x - 2) (x + 4)}$