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Cancel out the common factor of the numerator and denominator.

Common Factor of 3x^2 and 6x is 3x.

Hence we can write

3 x^2 / 6x = 3x *x / 3x * 2 = x /2

Answer: - Therefore, 3 x^2 / 6x = x / 2.

i) Factor the numerator.

Therefore (X^2 + 4 x + 4) = x^2 + 2 * x^2 * 2 + 2^2 = (x + 2)^2

[Since (a + b)^2 = a^2 + 2ab + b^2]

ii) Take the common factor of the denominator

Therefore (2 x + 4) = 2 (x + 2).

iii) Cancel out the common term of the numerator and denominator, therefore we can write,

(X^2 + 4 x + 4) / (2 x + 4) = (x + 2)^2 / 2 (x + 2) = (x + 2) / 2

(x^2 – 9) / (x^3 -9 x^2 +27 x – 9) = (x+3) (x - 3)/(x - 3) ^3 = (x+3)/(x-3) ^2