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ololo11 [35]
3 years ago
8

Pls help hella lost

Mathematics
1 answer:
irga5000 [103]3 years ago
4 0
L = -4,4
E = -2, -3
N = 2,1
I = 4,3
E = 1,3
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With some simple rearrangement, we can rewrite the numerator as

2x^3 - 3x^2 - x + 4 = 2(x^3 - x) - 3x^2 + x + 4 \\\\ ~~~~~~~~ = 2x(x^2-1) - 3(x^2 - 1) + x + 1 \\\\ ~~~~~~~~ = (2x-3)(x^2-1) + x+1

Then factorizing the difference of squares, x^2-1=(x-1)(x+1), we end up with

\dfrac{2x^3 - 3x^2 - x + 4}{x^2 - 1} = \dfrac{(2x-3)(x-1)(x+1) + x+1}{(x-1)(x+1)} \\\\ ~~~~~~~~ = \boxed{2x-3 + \dfrac1{x-1}}

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