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(2x^2-8x-42)/[(x^2-9)/(x^2-3x)]

=2(x^2-4x-21)/[(x+3)(x-3)/(x(x-3))]

=2(x-7)(x+3)/[(x+3)/x]

When we canceled out "(x-3)," it set up a domain restriction: x≠3. This is correct because we are not allowed to divide by 0 at any point, ever! Moving on...

=2(x-7)(x+3)(x)/(x+3)

=2(x-7)(x)

Now, x≠-3 for the same reason stated above. Moving on...

=2x(x-7)

=2x^2-14x

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13y ago

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