Divide. x² + 2x + 1 / x² - 1 ÷ ( 2x² + 2x ).

a. x + 1 / 2x

b. 2x(x + 1)² / x + 1

c. 1/2

d. 1 / 2x(x - 1 )

(x^{2} + 2x + 1)/(x^{2} – 1) ÷ (2x^{2} + 2x) = put the divisor into the denominator

(x^{2} + 2x + 1)/[(x^{2} – 1)(2x^{2} + 2x)] = factor by using gcd and formulas

(x + 1)^{2}/[(x + 1)(x – 1)2x(x + 1)] = cancel the common factors

1/[2x(x – 1)]

Answer: D

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