Đáp án:
$\begin{array}{l}
d)\dfrac{{{x^2} - {y^2} + 3x - 3y}}{{{x^2}y - x{y^2} - x + y}}\\
= \dfrac{{\left( {x - y} \right)\left( {x + y} \right) + 3\left( {x - y} \right)}}{{xy\left( {x - y} \right) - \left( {x - y} \right)}}\\
= \dfrac{{\left( {x - y} \right)\left( {x + y + 3} \right)}}{{\left( {x - y} \right)\left( {xy - 1} \right)}}\\
= \dfrac{{x + y + 3}}{{xy - 1}}\\
e)\dfrac{{{x^2} - 6xy + 9{y^2}}}{{{x^2} - 9{y^2}}}\\
= \dfrac{{{{\left( {x - 3y} \right)}^2}}}{{\left( {x - 3y} \right)\left( {x + 3y} \right)}}\\
= \dfrac{{x - 3y}}{{x + 3y}}\\
f)\dfrac{{{x^2} + x - 2}}{{{x^2} + 7x + 10}}\\
= \dfrac{{\left( {x + 2} \right)\left( {x - 1} \right)}}{{\left( {x + 2} \right)\left( {x + 5} \right)}}\\
= \dfrac{{x - 1}}{{x + 5}}
\end{array}$
