Discussion
Simplify (x - 9)(x + 10) ⁄ (x² - 81)
Answer: C
Factorise the denominator as a difference of squares, then cancel.
\[ x^{2} - 81 = (x-9)(x+9) \]
\[ \frac{(x-9)(x+10)}{(x-9)(x+9)} = \frac{x+10}{x+9} \]
The common factor \( (x-9) \) cancels, provided \( x \neq 9 \). Cancelling the wrong pair would leave \( \tfrac{x+10}{x-9} \).
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