Simplified form of $$\frac{x^2 - 5x + 6}{x ^2 - 7x + 10}\div \frac{x^2 - 10x + 21}{x^2 - 9x + 20}$$​​

Correct option is A

Given:

$$\frac{x^2 - 5x + 6}{x ^2 - 7x + 10}\div \frac{x^2 - 10x + 21}{x^2 - 9x + 20}$$ 

Solution: 

$$\frac{x^2 - 5x + 6}{x ^2 - 7x + 10}\div \frac{x^2 - 10x + 21}{x^2 - 9x + 20}$$  

Factor all quadratic expressions:

x² - 5x + 6 = (x - 2)(x - 3)

x² - 7x + 10 = (x - 2)(x - 5)

x² - 10x + 21 = (x - 3)(x - 7)

x² - 9x + 20 = (x - 4)(x - 5)

= $$\frac{x^2 - 5x + 6}{x ^2 - 7x + 10}\times\frac{x^2 - 9x + 20}{x^2 - 10x + 21}$$ 

= $$\frac{ (x - 2)(x - 3)}{ (x - 2)(x - 5)} \times \frac{(x - 4)(x - 5)}{ (x - 3)(x - 7)}$$ 

= $$\frac{x-4}{x-7}$$​