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Answer
The simplified expression is \( x - 4 \), provided that \( x \neq 0 \).
Solution
To simplify the expression (2x² - 8x) / (2x), follow these steps:
1. Factor the numerator: 2x² - 8x = 2x(x - 4).
2. Write the expression as [2x(x - 4)] / (2x).
3. Cancel the common factor 2x (provided x ≠ 0) to obtain x - 4.
Thus, the simplified expression is x - 4, with the condition that x ≠ 0.
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Simplify this solution Bonus Knowledge
To simplify the expression \( \frac{2 x^{2}-8 x}{2 x} \), first, we can factor out the numerator: \( 2x^2 - 8x = 2x(x - 4) \). Now, substituting this back into the fraction gives us: \( \frac{2x(x - 4)}{2x} \). The \( 2x \) in the numerator and the \( 2x \) in the denominator cancel out, provided \( x \neq 0 \): \( x - 4 \). Thus, the simplified expression is: \( x - 4 \).
