Question

Solve the following expression: \[ \frac{x}{x - 1} \times \frac{x + 1}{x} \]

• A. \(2\)
• B. \(0\)
• C. \(1\)
• D. \(-1\)

Hint:

When simplifying rational expressions, always check for restrictions on the variable. In this case, the expression \[ \frac{x - 1}{x + 1} \] is undefined at \( x = -1 \), since division by zero occurs. Even after simplifying, make sure to account for values that make the denominator zero, as these lead to undefined results.

Answer 1

The Correct Option is C

We need to simplify the expression: \[ \frac{x}{x - 1} \times \frac{x + 1}{x} \] First, cancel out the \(x\) terms in the numerator and denominator: \[ \frac{x + 1}{x - 1} \] So, the simplified expression is: \[ \frac{x + 1}{x - 1} \] Now, substituting \(x = 1\) into this expression: \[ \frac{1 + 1}{1 - 1} = \frac{2}{0} \] which is undefined. Thus, the simplified result is not 1. The value depends on the context given.