Reduce to lowest terms: (Equation In Comments)

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Reduce to lowest terms: (Equation In Comments)

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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\[\frac{ 2^{2}-3x-2 }{ 10+x-3x ^{2} }\]
Thats 2x to the second power above sorry
The numerator 2x^2 -3x -2 can be factored by grouping: The coefficient of 2 multiplied by -2 = -4. We need 2 numbers so that when multiplied = -4 and the sum = -3. (-3x is the 2nd term in the numerator.) 1(-4) = -4 1-4 =-3 Since -4x + 1x = -3x This can be re-written as 2x^2 -4x +x -2 when factored by grouping we get 2x(x - 2) +1(x - 2) when factored further we get (2x + 1)(x -2)

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Other answers:

The denominator can be re-written as -3x^2 + x + 10 -3(10) = -30 -5(6) = -30 -5 + 6 = 1 Therefore it can be re-written as -3x^2 +6x -5x + 10 When factored it equals -3x(x - 2) -5(x - 2) When factored further it equals (-3x - 5)(x - 2)
So we get \[\frac{ (2x + 1)(x - 2) }{ -1(3x + 5)(x -2) }\] the x - 2 in the numerator and denominator cancel each other out
Thank you very much!

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