Question

simplify the expression \\(\frac{1}{1 + \left(\frac{1 - x}{x}\
ight)}\\)

Explanation:

Step1: Simplify the denominator

First, simplify the expression in the denominator: \(1 + \frac{1 - x}{x}\). To add these terms, find a common denominator, which is \(x\). So we have \(\frac{x}{x}+\frac{1 - x}{x}=\frac{x+(1 - x)}{x}\). Simplifying the numerator: \(x + 1 - x=1\). So the denominator simplifies to \(\frac{1}{x}\).

Step2: Divide by the simplified denominator

Now our original expression \(\frac{1}{1+\frac{1 - x}{x}}\) becomes \(\frac{1}{\frac{1}{x}}\). Dividing by a fraction is the same as multiplying by its reciprocal, so \(\frac{1}{\frac{1}{x}} = 1\times x=x\) (assuming \(x
eq0\) and \(x
eq1\) to avoid division by zero in the original expression).

Answer:

\(x\)