Đáp án:
2) \(\dfrac{{2x}}{{x + 2y}}\)
Giải thích các bước giải:
\(\begin{array}{l}
1)\dfrac{y}{{x\left( {2x - y} \right)}} + \dfrac{{4x}}{{y\left( {y - 2x} \right)}}\\
= \dfrac{{{y^2} - 4{x^2}}}{{xy\left( {2x - y} \right)}}\\
= \dfrac{{\left( {y - 2x} \right)\left( {y + 2x} \right)}}{{xy\left( {2x - y} \right)}}\\
= - \dfrac{{y + 2x}}{{xy}}\\
3)\dfrac{{4\left( {x - 2} \right) + 2\left( {x + 2} \right) - 5x + 6}}{{\left( {x - 2} \right)\left( {x + 2} \right)}}\\
= \dfrac{{4x - 8 + 2x + 4 - 5x + 6}}{{\left( {x - 2} \right)\left( {x + 2} \right)}}\\
= \dfrac{{x + 2}}{{\left( {x - 2} \right)\left( {x + 2} \right)}} = \dfrac{1}{{x - 2}}\\
2)\dfrac{{x\left( {x + 2y} \right) + x\left( {x - 2y} \right) - 4xy}}{{\left( {x - 2y} \right)\left( {x + 2y} \right)}}\\
= \dfrac{{{x^2} + 2xy + {x^2} - 2xy - 4xy}}{{\left( {x - 2y} \right)\left( {x + 2y} \right)}}\\
= \dfrac{{2{x^2} - 4xy}}{{\left( {x - 2y} \right)\left( {x + 2y} \right)}} = \dfrac{{2x\left( {x - 2y} \right)}}{{\left( {x - 2y} \right)\left( {x + 2y} \right)}}\\
= \dfrac{{2x}}{{x + 2y}}\\
4)\dfrac{{5\left( {5x + 5} \right) - x\left( {25 - x} \right)}}{{5x\left( {x - 5} \right)}}\\
= \dfrac{{25x + 25 - 25x + {x^2}}}{{5x\left( {x - 5} \right)}}\\
= \dfrac{{{x^2} + 25}}{{5x\left( {x - 5} \right)}}
\end{array}\)
