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2. -1
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\[\dfrac{9x}{x-x^2}\] Simplify the following: \[\dfrac{-9 x}{x-x^2}\] Factor common terms out of \(x-x^2.\) Factor -x out of \(x-x^2:\) \[\dfrac{-9 x}{-x (x-1)}\] Cancel common terms in the numerator and denominator of \(\frac{-9 x}{-x (x-1)}\). \[\dfrac{-9 x}{-x (x-1)} = \dfrac{x}{x}\times \dfrac{-9}{-(x-1)} = \dfrac{-9}{-(x-1)}:\] \[\dfrac{-9}{-(x-1)}\] Simplify the sign of \(\dfrac{-9}{-(x-1)}\). Multiply numerator and denominator of \(\dfrac{-9}{-(x-1)}\) by -1: Answer: \(\dfrac{9}{(x-1)}\)
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