If $$\frac{m}{n}{\text{ = }}\frac{4}{3}$$   and $$\frac{r}{t}{\text{ = }}\frac{9}{{14}}{\text{,}}$$   then the value of $$\frac{{3mr - nt}}{{4nt - 7mr}}{\text{ is}} = {\text{?}}$$

$$\eqalign{ & \frac{m}{n}{\text{ = }}\frac{4}{3}{\text{ and }}\frac{r}{t}{\text{ = }}\frac{9}{{14}} \cr & \Rightarrow \frac{{mr}}{{nt}} = \frac{4}{3} \times \frac{9}{{14}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{6}{7} \cr & \therefore \frac{{3mr - nt}}{{4nt - 7mr}}{\text{ }} \cr & = \frac{{3\frac{{mr}}{{nt}} - 1}}{{4 - 7\frac{{mr}}{{nt}}}} \cr & = \frac{{3 \times \frac{6}{7} - 1}}{{4 - 7 \times \frac{6}{7}}} \cr & = \frac{{\frac{{18}}{7} - 1}}{{4 - 6}} \cr & = \frac{{11}}{7} \times \left( { - \frac{1}{2}} \right) \cr & = - \frac{{11}}{{14}} \cr} $$