Problem: The expression x2−3x+2x2−5x+6÷x2−5x+4x2−7x+12\dfrac{x^{2}-3 x+2}{x^{2}-5 x+6} \div \dfrac{x^{2}-5 x+4}{x^{2}-7 x+12}x2−5x+6x2−3x+2÷x2−7x+12x2−5x+4, when simplified, is:
Answer Choices:
A. (x−1)(x−6)(x−3)(x−4)\dfrac{(x-1)(x-6)}{(x-3)(x-4)}(x−3)(x−4)(x−1)(x−6)
B. x+3x−3\dfrac{x+3}{x-3}x−3x+3
C. x+1x−1\dfrac{x+1}{x-1}x−1x+1
D. 111
E. 222 Solution:
(x−2)(x−1)(x−3)(x−2)⋅(x−3)(x−4)(x−4)(x−1)=1\dfrac{(x-2)(x-1)}{(x-3)(x-2)} \cdot \dfrac{(x-3)(x-4)}{(x-4)(x-1)}=1 (x−3)(x−2)(x−2)(x−1)⋅(x−4)(x−1)(x−3)(x−4)=1