Giải thích các bước giải:
$\begin{gathered} f)\,(\,\frac{{5x + y}}{{{x^2} - 5xy}} + \frac{{5x - y}}{{{x^2} + 5xy}}).\frac{{{x^2} - 25{y^2}}}{{{x^2} + {y^2}}} \hfill \\ = \frac{{(5x + y)(x + 5y) + (5x - y)(x - 5y)}}{{x(x - 5y)(x + 5y)}}.\frac{{(x - 5y)(x + 5y)}}{{{x^2} + {y^2}}} \hfill \\ = \frac{{5{x^2} + xy + 25xy + 5{y^2} + 5{x^2} - xy - 25xy + 5{y^2}}}{{x(x - 5y)(x + 5y)}}.\frac{{(x - 5y)(x + 5y)}}{{{x^2} + {y^2}}} \hfill \\ = \frac{{10{x^2} + 10{y^2}}}{{x({x^2} + {y^2})}} \hfill \\ = \frac{{10}}{x} \hfill \\ \end{gathered} $
$\begin{gathered} g)\,\frac{{{x^2} + x}}{{5{x^2} - 10x + 5}}:\frac{{3x + 3}}{{5x - 5}} \hfill \\ = \frac{{x(x + 1)}}{{5({x^2} - 2x + 1)}}.\frac{{5(x - 1)}}{{3(x + 1)}} \hfill \\ = \frac{{x(x - 1)}}{{3{{(x - 1)}^2}}} \hfill \\ = \frac{x}{{3(x - 1)}} \hfill \\ \end{gathered} $
$\begin{gathered} k)\,\frac{3}{{2x + 6}} - \frac{{x - 6}}{{2{x^2} + 6x}} \hfill \\ = \frac{{3x - (x - 6)}}{{x(2x + 6)}} \hfill \\ = \frac{{3x - x + 6}}{{x(2x + 6)}} \hfill \\ = \frac{{2x + 6}}{{x(2x + 6)}} \hfill \\ = \frac{1}{x} \hfill \\ \end{gathered} $
$\begin{gathered} m)\,\frac{{2x + 6}}{{3{x^2} - x}}:\frac{{{x^2} + 3x}}{{1 - 3x}} \hfill \\ = \frac{{2(x + 3)}}{{x(3x - 1)}}.\frac{{1 - 3x}}{{x(x + 3)}} \hfill \\ = \frac{{ - 2}}{{{x^2}}} \hfill \\ \end{gathered} $
