Giải thích các bước giải:
$\begin{array}{l} \left( {\frac{{x + 2}}{{x + 1}} - \frac{{2x}}{{x - 1}}} \right).3x + \frac{3}{x} + 4{x^2} + \frac{{x + 7}}{{{x^2} - x}}\\ = \left( {\frac{{(x + 2)(x - 1) - 2x(x + 1)}}{{(x + 1)(x - 1)}}} \right).3x + \frac{3}{x} + 4{x^2} + \frac{{x + 7}}{{{x^2} - x}}\\ = \frac{{{x^2} + x - 2 - (2{x^2} - 2x)}}{{(x + 1)(x - 1)}}.3x + \frac{3}{x} + 4{x^2} + \frac{{x + 7}}{{{x^2} - x}}\\ = \frac{{ - {x^2} + 3x - 2}}{{(x + 1)(x - 1)}}.3x + \frac{3}{x} + 4{x^2} + \frac{{x + 7}}{{{x^2} - x}}\\ = \frac{{ - (x - 2)(x - 1)}}{{(x + 1)(x - 1)}}.3x + \frac{3}{x} + 4{x^2} + \frac{{x + 7}}{{{x^2} - x}}\\ = \frac{{ - 3x(x - 2)}}{{x + 1}} + \frac{3}{x} + 4{x^2} + \frac{{x + 7}}{{{x^2} - x}}\\ = \frac{{( - 3{x^2} + 6x)({x^2} - x) + 3({x^2} - x) + 4{x^2}({x^3} - {x^2}) + (x + 7)(x + 1)}}{{x(x - 1)(x + 1)}}\\ = \frac{{4{x^5} - 7{x^4} + 9{x^3} - 2{x^2} + 5x + 7}}{{x(x - 1)(x + 1)}} \end{array}$
