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Verified Answer :

dcruse

Simplifying
(2x2 + -3x + 1)(x + -2)

Reorder the terms:
(1 + -3x + 2x2)(x + -2)

Reorder the terms:
(1 + -3x + 2x2)(-2 + x)

Multiply (1 + -3x + 2x2) (-2 + x)
(1(-2 + x) + -3x (-2 + x) + 2x2 (-2 + x))
((-2 1 + x 1) + -3x (-2 + x) + 2x2 (-2 + x))
((-2 + 1x) + -3x (-2 + x) + 2x2 (-2 + x))
(-2 + 1x + (-2 -3x + x -3x) + 2x2 (-2 + x))
(-2 + 1x + (6x + -3x2) + 2x2 (-2 + x))
(-2 + 1x + 6x + -3x2 + (-2 2x2 + x * 2x2))
(-2 + 1x + 6x + -3x2 + (-4x2 + 2x3))

Combine like terms: 1x + 6x = 7x
(-2 + 7x + -3x2 + -4x2 + 2x3)

Combine like terms: -3x2 + -4x2 = -7x2
(-2 + 7x + -7x2 + 2x3)

Factor the bottom (x + 1)(x - 3)
now the fraction looks like (x - 3)/((x + 1)(x - 3))
the (x-3)'s cancel out leaving 1/(x + 1) or D

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