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Simplify 1x2+5x+6 + \(\frac{1}{x^2 + 3x + ...

Simplify 1x2+5x+6 + 1x2+3x+2

A.

x(x+2)(x3)

B.

2(x+5)(x3)

C.

2(x+1)(x+3)

D.

2(x1)(x3)

Correct answer is C

1x2+5x+6 + 1x2+3x+2 = 1(x+1)(x+2) + 1(x+1)(x+1)

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

2x+4(x+1)(x+2)(x+3) = 2(x+2)(x+1)(x+2)(x+3)

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