Given

$\frac{(x^2-5x+6)}{(x^2-7x+12)}=\frac{(x^2-x-6)}{(x^2+7x+10)}$, then the value of $x$ is

The correct option is C: $2.2$

The given equation is

$\frac{x^2-5x+6}{x^2-7x+12}=\frac{x^2-x-6}{x^2+7x+10}$

$\Rightarrow \frac{x^2-3x-2x+6}{x^2-4x-3x+12}=\frac{x^2-3x+2x-6}{x^2+5x+2x+10}$

$\Rightarrow \frac{x(x-3)-2(x-3)}{x(x-4)-3(x-4)}=\frac{x(x-3)+2(x-3)}{x(x+5)+2(x+5)}$

$\Rightarrow \frac{(x-3)(x-2)}{(x-3)(x-4)}=\frac{(x-3)(x+2)}{(x+5)(x+2)}$

$\Rightarrow \frac{x-2}{x-4}=\frac{x-3}{x+5}$

$\left[\text{cancelling same polynomial from numerator and denomintor}\right]$

$\Rightarrow (x-2)(x+5)=(x-4)(x-3)$

$\Rightarrow x^2+5x-2x-10=x^2-3x-4x+12$

$\Rightarrow x^2+3x-10=x^2-7x+12$

$\Rightarrow 10x=22$

$\therefore x=2.2$