Quadratic Equations
Extraneous Roots
Premium Question
Grade 11

Question:

The equation $x - \frac{2}{x - 1} = 1 - \frac{2}{x - 1}$ has:
(1) no real root
(2) one real root
(3) two equal real roots
(4) infinitely many roots

Step-by-Step Solution

Key Concept: Note that $-2/(x - 1)$ appears on both sides. If you cancel it (valid for $x \neq 1$), what equation do you get for $x$? Is that consistent with the domain?
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)

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