X2-7x-10x2-5x-14-x3-8x3-8-x2-2x-4x2-2x-4-x-7x-5-

x^2 7x+10/x^2 5x 14×x^3+8/x^3 8×x^2+2x+4/x^2 2x+4×x 7/x 5 x^2 2x 5x+10/x^2 7x+2x 14×x^3+8/x^3 8×x^2+2x+4/x^2 2x+4×x 7/x 5 (x 2)(x 5)/(x 7)(x+2)×x ...

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Distributive Property of Multiplication

x2-7x+10x2-5x...

Question

$\frac{x^{2} - 7 x + 10}{x^{2} - 5 x - 14} \times \frac{x^{3} + 8}{x^{3} - 8} \times \frac{x^{2} + 2 x + 4}{x^{2} - 2 x + 4} \times \frac{x - 7}{x - 5} = ?$

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Solution

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\frac{x^{2} - x - 1}{x^{3} - 8} = \frac{A}{x - 2} + \frac{B x + C}{x^{2} + 2 x + 4} \Rightarrow A + B =

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lim x \to 1 [\frac{x^{2} + 1}{x + 100}]

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