If $\alpha$ and $\beta$ are the roots of the equation,
7x² – 3x – 2 = 0, then the value of
${\alpha \over {1 - {\alpha ^2}}} + {\beta \over {1 - {\beta ^2}}}$ is equal to :

Given, 7x² – 3x – 2 = 0 <br><br>$\therefore$ $\alpha$ + $\beta$ = ${3 \over 7}$ <br><br>$\alpha$$\beta$ = - ${2 \over 7}$ <br><br>${\alpha \over {1 - {\alpha ^2}}} + {\beta \over {1 - {\beta ^2}}}$ <br><br>= $${{\alpha + \beta - \alpha \beta \left( {\alpha + \beta } \right)} \over {1 - {\alpha ^2} - {\beta ^2} + {\alpha ^2}{\beta ^2}}}$$ <br><br>= $${{{3 \over 7} + {2 \over 7}\left( {{3 \over 7}} \right)} \over {1 - {{\left( {\alpha + \beta } \right)}^2} + 2\alpha \beta + {{\left( { - {2 \over 7}} \right)}^2}}}$$ <br><br>= $${{{3 \over 7} + {2 \over 7}\left( {{3 \over 7}} \right)} \over {1 - {{\left( {{3 \over 7}} \right)}^2} + 2\left( { - {2 \over 7}} \right) + {{\left( { - {2 \over 7}} \right)}^2}}}$$ <br><br>= ${{27} \over {16}}$