To simplify the expression \((\frac{1}{x} + \frac{2}{x-1}) / (\frac{4}{x} - 1)\), we will work step by step.
First, simplify the numerator:
\[ \frac{1}{x} + \frac{2}{x-1} \]
To combine these fractions, we need a common denominator. The common denominator is \(x(x-1)\).
Rewriting each term under this common denominator gives:
\[ \frac{1}{x} = \frac{(x-1)}{x(x-1)} \] \[ \frac{2}{x-1} = \frac{2x}{x(x-1)} \]
Now combine:
\[ \frac{(x-1) + 2x}{x(x-1)} = \frac{3x - 1}{x(x-1)} \]
Now we simplify the denominator:
\[ \frac{4}{x} - 1 \]
Again, let's rewrite \(1\) under the same denominator \(x\):
\[ 1 = \frac{x}{x} \]
Thus, we write:
\[ \frac{4}{x} - 1 = \frac{4 - x}{x} \]
Now we substitute both parts back into the original expression:
\[ \frac{\frac{3x - 1}{x(x-1)}}{\frac{4 - x}{x}} \]
Dividing by a fraction is equivalent to multiplying by its reciprocal:
\[ \frac{3x - 1}{x(x-1)} \cdot \frac{x}{4 - x} \]
The \(x\) in the numerator of the second fraction cancels with \(x\) in the denominator of the first fraction, assuming \(x \neq 0\):
\[ \frac{3x - 1}{(x-1)(4 - x)} \]
So the simplified expression is:
\[ \frac{3x - 1}{(x-1)(4 - x)} \]
And that is the final answer:
\[ \frac{3x - 1}{(x-1)(4 - x)} \]