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Common factor of x ^4 and 3 x^2 is x^2. Therefore

x ^ 4 / 3 x ^2 = x ^2 * x ^2 / 3 * x ^2 = x^2 / 3

Therefore x ^ 4 / 3 x ^2 = x^2 / 3

i) X ^2 – 2 x = x ( x – 2)

ii) X ^ 2 – 4 = x ^2 – 2 ^2 = (x + 2) (x – 2)

Therefore, (x ^2 – 2 x) / (x ^2 – 4) = x ( x – 2) / (x + 2) (x – 2) = x / x + 2

(x^3 + 3 x^2 + 3 x + 1) / (x ^2 + 2 x + 1)

= (x ^3 + 3 * x^2* 1 + 3 * x * 1^2 + 1 ^3) / (x ^2 + 2 * x * 1 + 1 ^2)

= (x + 1) ^3 / (x +1)^2

= (x+1)