# Given f(x)=1/(x-1), and g(x)=2/x, how do you find f(g(x))?

Jun 4, 2017

$f \left(g \left(x\right)\right) = \frac{x}{2 - x}$

#### Explanation:

To find f(g(x)), simply plug g(x) into x in the equation for f(x):
$f \left(g \left(x\right)\right) = \frac{1}{\left(\frac{2}{x}\right) - 1}$
Simplify this by finding a common denominator for the denominator:
1/((2/x)-(x/x)
Simplify: $\frac{1}{\frac{2 - x}{x}}$
Clear the fraction by using keep-change-flip: $1 \cdot \left(\frac{x}{2 - x}\right)$
Simplify: $f \left(g \left(x\right)\right) = \frac{x}{2 - x}$