What is (x^2-3x+2)/(x^2-5x +6)÷(x^2-5x+4)/(x^2-7x+12) equal to?

Question

What is \(\frac{x^2-3x+2}{x^2-5x+6}\) ÷  \(\frac{x^2-5x+4}{x^2-7x+12}\) equal to? equal to?

(a) \(\frac{x+3}{x-3}\) 

(b) 1 

(c) \(\frac{x+1}{x-1}\)

(d) 2

Answer 1

(b) 1

\(\frac{x^2-3x+2}{x^2-5x+6}\) ÷ \(\frac{x^2-5x+4}{x^2-7x+12}\)

= \(\frac{(x-1)(x-2)}{(x-3)(x-2)} ÷ \frac{(x-4)(x-1)}{(x-3)(x-4)}\)

= \(\frac{(x-1)}{(x-3)}\) ÷ \(\frac{(x-1)}{(x-3)}\) = \(\frac{(x-1)}{(x-3)}\) x \(\frac{(x-3)}{(x-1)}\) = 1.