b
(b) \({{3x} \over {(x - 2)\,(x + 1)}} = - {{3x} \over 2}{(1 + x)^{ - 1}}{\left( {1 - {x \over 2}} \right)^{ - 1}} = - {3 \over 2}x\)

\((1 - x + {x^2} - {x^3} + {x^4} - ..)\,\left( {1 + {x \over 2} + {{\left( {{x \over 2}} \right)}^2} + {{\left( {{x \over 2}} \right)}^3} + ...} \right)\)

Coefficient of \({x^4} = - {3 \over 2}\left[ { - 1.1 + 1.{1 \over 2} - 1.{1 \over 4} + 1.{1 \over 8}} \right]\)

\( = - {3 \over 2}\,\left[ { - 1 + {1 \over 2} - {1 \over 4} + {1 \over 8}} \right] = {{15} \over {16}}\).