What is the simplified version of x-3/x^2-2x-3?

A) x-3/x^2-2x-3

B) x/x^2-2x

C) 1/x-2

D) 1/x+1

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