\(a)\frac{{5 - 3{\rm{x}}}}{{x + 1}} - \frac{{ - 2 + 5{\rm{x}}}}{{x + 1}} = \frac{{5 - 3{\rm{x - }}\left( { - 2 + 5{\rm{x}}} \right)}}{{x + 1}} = \frac{{5 - 3{\rm{x}} + 2 - 5{\rm{x}}}}{{x + 1}} = \frac{{7 - 8{\rm{x}}}}{{x + 1}}\)
\(b)\frac{x}{{x - y}} - \frac{y}{{x + y}} = \frac{{x\left( {x + y} \right) - y\left( {x - y} \right)}}{{\left( {x - y} \right)\left( {x + y} \right)}} = \frac{{{x^2} + xy - xy + {y^2}}}{{\left( {x - y} \right)\left( {x + y} \right)}} = \frac{{{x^2} + {y^2}}}{{\left( {x - y} \right)\left( {x + y} \right)}}\)
\(\begin{array}{l}c)\frac{3}{{x + 1}} - \frac{{2 + 3{\rm{x}}}}{{{x^3} + 1}} \\ = \frac{3}{{x + 1}} - \frac{{2 + 3{\rm{x}}}}{{\left( {x + 1} \right)\left( {{x^2} - x + 1} \right)}}\\ = \frac{{3\left( {{x^2} - x + 1} \right) - 2 - 3{\rm{x}}}}{{\left( {x + 1} \right)\left( {{x^2} - x + 1} \right)}}\\ = \frac{{3{{\rm{x}}^2} - 3{\rm{x}} + 3 - 2 - 3{\rm{x}}}}{{\left( {x + 1} \right)\left( {{x^2} - x + 1} \right)}} = \frac{{3{{\rm{x}}^2} - 6{\rm{x}} + 1}}{{\left( {x + 1} \right)\left( {{x^2} - x + 1} \right)}}\end{array}\)