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The simplified expression is \( \frac{1}{4} \), provided that \( x \neq 2 \).
Solución
To simplify the expression (x - 2) / (4x - 8), follow these steps:
1. Factor the denominator: 4x - 8 = 4(x - 2).
2. Rewrite the expression as (x - 2) / [4(x - 2)].
3. Cancel the common factor (x - 2), noting that x ≠ 2 (since division by zero is undefined).
The simplified expression is 1/4, with the condition x ≠ 2.
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Simplifique esta solución The Deep Dive
To simplify the expression \( \frac{x-2}{4x-8} \), first notice that the denominator can be factored. The term \( 4x-8 \) can be rewritten as \( 4(x-2) \). So, we have: \[ \frac{x-2}{4(x-2)} \] Now, cancel out the \( x-2 \) from the numerator and the denominator (as long as \( x \neq 2 \) since that would make the original expression undefined): \[ \frac{1}{4} \] Thus, the simplified expression is \( \frac{1}{4} \).
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