To simplify the expression \((5 - 5x) / (x^2 - 1)\), we can first factor both the numerator and the denominator, if possible.
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Factor the numerator: \[ 5 - 5x = 5(1 - x) \]
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Factor the denominator: The expression \(x^2 - 1\) is a difference of squares, which can be factored as: \[ x^2 - 1 = (x - 1)(x + 1) \]
Now, substitute the factored forms back into the expression:
\[ \frac{5(1 - x)}{(x - 1)(x + 1)} \]
Next, notice that \(1 - x\) can be rewritten as \(-(x - 1)\):
\[ 1 - x = -(x - 1) \]
Substituting this in, we get:
\[ \frac{5(-1)(x - 1)}{(x - 1)(x + 1)} = \frac{-5(x - 1)}{(x - 1)(x + 1)} \]
Assuming \(x \neq 1\) (because at \(x = 1\) the expression is undefined), we can cancel out the \((x - 1)\) terms in the numerator and denominator:
\[ \frac{-5}{x + 1} \]
Therefore, the simplified form of the expression \((5 - 5x) / (x^2 - 1)\) is:
\[ \frac{-5}{x + 1} \quad \text{for } x \neq 1 \]