Question 88

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

Solution

Expression : $$\frac{(x^{2}-5x+6)}{(x^{2}-3x+2)}\div\frac{(x^{2}-7x+12)}{(x^{2}-5x+4)}$$

Here, $$x^2-5x+6 = x^2-3x-2x+6$$

= $$x(x-3)-2(x-3)=(x-2)(x-3)$$

Similarly for other terms, we get :

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

= $$\frac{x-3}{x-1}\times\frac{x-1}{x-3}$$

= $$1$$

=> Ans - (A)

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