Find f(g(x)) f(x)=5/(x-3) , g(x)=2/(7x)

$f (x) = \frac{5}{x - 3}$ , $g (x) = \frac{2}{7 x}$

Set up the composite result function.

$f (g (x))$

Evaluate $f (\frac{2}{7 x})$ by substituting in the value of $g$ into $f$ .

$f (\frac{2}{7 x}) = \frac{5}{(\frac{2}{7 x}) - 3}$

Simplify the denominator.

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{7 x}{7 x}$ .

$f (\frac{2}{7 x}) = \frac{5}{\frac{2}{7 x} - 3 \cdot \frac{7 x}{7 x}}$

Combine $- 3$ and $\frac{7 x}{7 x}$ .

$f (\frac{2}{7 x}) = \frac{5}{\frac{2}{7 x} + \frac{- 3 (7 x)}{7 x}}$

Combine the numerators over the common denominator.

$f (\frac{2}{7 x}) = \frac{5}{\frac{2 - 3 (7 x)}{7 x}}$

Multiply $- 3$ by $7$ .

$f (\frac{2}{7 x}) = \frac{5}{\frac{2 - 21 x}{7 x}}$

Multiply the numerator by the reciprocal of the denominator.

$f (\frac{2}{7 x}) = 5 (\frac{7 x}{2 - 21 x})$

Multiply $5 \frac{7 x}{2 - 21 x}$ .

Combine $5$ and $\frac{7 x}{2 - 21 x}$ .

$f (\frac{2}{7 x}) = \frac{5 (7 x)}{2 - 21 x}$

Multiply $7$ by $5$ .

$f (\frac{2}{7 x}) = \frac{35 x}{2 - 21 x}$