Solve the equation (x^2 - 5x + 6)/(x - 2) = x - 1, finding all real solutions.

Solve the equation $\frac{x ^{2} - 5 x + 6}{x - 2} = x - 1$ , finding all real solutions.

hard 4 marks Class 8 · Mathematics · Algebraic Expressions and Identities

Answer

No real solution

The correct answer is No real solution — Hence there is no real value of $x$ that satisfies the equation; $x = 2$ is excluded due to division by zero.

Step-by-step solution

Factor the numerator: $x^{2} - 5 x + 6 = (x - 2) (x - 3)$ .
Cancel the common factor $(x - 2)$ with the denominator, remembering that $x e q 2$ .
The equation reduces to $x - 3 = x - 1$ .
Subtract $x$ from both sides: $- 3 = - 1$ , which is impossible.
Hence there is no real value of $x$ that satisfies the equation; $x = 2$ is excluded due to division by zero.

Common mistake: Cancelling

(x - 2)

and mistakenly including

x = 2

as a solution

Concept tested: Simplifying rational expressions

Published 4 October 2026 · How this solution was prepared and checked

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Solve the equation x−2x2−5x+6​=x−1, finding all real solutions.

Step-by-step solution

Solve the equation $\frac{x ^{2} - 5 x + 6}{x - 2} = x - 1$ , finding all real solutions.