If $${x^2} + 5x + 6 = 0{\text{,}}$$    then the value of $$\frac{{2x}}{{{x^2} - 7x + 6}}$$   is?

Solution (By Examveda Team)

$$\eqalign{ & {\text{If }}{x^2} + 5x + 6 = 0 \cr & {\text{then, }}{x^2} + 6 = - 5x \cr & {\text{So,}}\frac{{2x}}{{{x^2} + 6 - 7x}} \cr & = \frac{{2x}}{{ - 5x - 7x}} \cr & = \frac{{2x}}{{ - 12x}} \cr & = - \frac{1}{6}{\text{ }} \cr} $$