Which is the correct simplification of (2x^2 - 4x)/(2x)?

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Multiple Choice

Which is the correct simplification of (2x^2 - 4x)/(2x)?

Explanation:
Reducing a fraction by factoring and canceling common factors is the idea here. Factor the numerator: 2x^2 − 4x = 2x(x − 2). The denominator is 2x. Cancel the common factor 2x, leaving x − 2. This reduction is valid for all x except x ≠ 0, since the original expression would be undefined at x = 0. Checking with a value like x = 3 gives (2·9 − 4·3)/(2·3) = (18 − 12)/6 = 6/6 = 1, and the simplified form x − 2 yields 3 − 2 = 1, confirming the result. The correct simplification is x − 2.

Reducing a fraction by factoring and canceling common factors is the idea here. Factor the numerator: 2x^2 − 4x = 2x(x − 2). The denominator is 2x. Cancel the common factor 2x, leaving x − 2. This reduction is valid for all x except x ≠ 0, since the original expression would be undefined at x = 0. Checking with a value like x = 3 gives (2·9 − 4·3)/(2·3) = (18 − 12)/6 = 6/6 = 1, and the simplified form x − 2 yields 3 − 2 = 1, confirming the result. The correct simplification is x − 2.

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