Giải thích các bước giải:
$\begin{array}{l}
1)\dfrac{{4{x^2} - 4xy}}{{5{x^3} - 5{x^2}y}}\left( {DK:x \ne 0;x \ne y} \right)\\
= \dfrac{{4x\left( {x - y} \right)}}{{5{x^2}\left( {x - y} \right)}}\\
= \dfrac{4}{{5x}}\\
2)\dfrac{{2a{x^2} - 4ax + 2a}}{{5b - 5b{x^2}}}\left( {DK:b \ne 0;x \ne \pm 1} \right)\\
= \dfrac{{2a\left( {{x^2} - 2x + 1} \right)}}{{5b\left( {1 - {x^2}} \right)}}\\
= \dfrac{{2a{{\left( {x - 1} \right)}^2}}}{{5b\left( {1 - x} \right)\left( {1 + x} \right)}}\\
= \dfrac{{2a\left( {1 - x} \right)}}{{5b\left( {1 + x} \right)}}\\
3)\dfrac{{4{x^5}{y^6}}}{{18x{y^7}}}\left( {DK:x,y \ne 0} \right)\\
= \dfrac{{4.x{y^6}.{x^4}}}{{18.x{y^6}.y}}\\
= \dfrac{{2{x^4}}}{{9y}}\\
4)\dfrac{{{x^2} + 5x + 6}}{{x + 3}}\left( {DK:x \ne - 3} \right)\\
= \dfrac{{\left( {x + 2} \right)\left( {x + 3} \right)}}{{x + 3}}\\
= x + 2\\
5)\dfrac{{{x^2} + 7x + 10}}{{{x^2} + 5x + 6}}\\
= \dfrac{{\left( {x + 2} \right)\left( {x + 5} \right)}}{{\left( {x + 2} \right)\left( {x + 3} \right)}}\\
= \dfrac{{x + 5}}{{x + 3}}
\end{array}$
