Discussion

Simplify (1 ⁄ (x² - 1)) ÷ (1 ⁄ (x + 1))

Answer: A

Dividing by a fraction means multiplying by its reciprocal.

\[ \frac{1}{x^{2}-1} \div \frac{1}{x+1} = \frac{1}{x^{2}-1} \times (x+1) \]

Factorising the denominator:

\[ = \frac{x+1}{(x-1)(x+1)} = \frac{1}{x-1} \]

The \( (x+1) \) cancels, which is why the difference of squares has to be split before the simplification becomes visible.

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