Đáp án + Giải thích các bước giải:

$\textbf{a}\bigg)$

$\begin{array}{l} & \dfrac{5y -xy}{x^2 -25}(x \ne \pm 5)
\\ &= \dfrac{-y(x - 5)}{(x + 5)(x - 5)}
\\ &= \dfrac{-y}{x + 5}\end{array}$

$\textbf{b}\bigg)$

$\begin{array}{l} & \dfrac{9 + 6x + x^2}{3x + 9}(x \ne -3)
\\ &= \dfrac{(x + 3)^2}{3(x + 3)}
\\ &= \dfrac{x + 3}{3}\end{array}$

$\textbf{c}\bigg)$

$\begin{array}{l} & \dfrac{2x^3y + 2xy^3}{x^4 - y^4}(x \ne \pm y)
\\ &= \dfrac{2xy(x^2 + y^2)}{(x^2 + y^2)(x^2 - y^2)}
\\ &= \dfrac{2xy}{x^2 - y^2}\end{array}$

$\textbf{d}\bigg)$

$\begin{array}{l} & \dfrac{2 - 4x}{4x^2 - 4x + 1}\left(x \ne \dfrac{1}{2}\right)
\\ &= \dfrac{2(1 - 2x)}{(2x - 1)^2}
\\ &= \dfrac{-2(2x - 1)}{(2x - 1)^2}
\\ &= \dfrac{-2}{2x - 1}\end{array}$

$\textbf{e}\bigg)$

$\begin{array}{l} & \dfrac{x - 2}{x^3 - 8}(x \ne 2)
\\ &= \dfrac{x - 2}{x^3 - 2^3}
\\ &= \dfrac{x - 2}{(x - 2)(x^2 + 2x + 4)}
\\ &= \dfrac{1}{x^2 + 2x + 4}\end{array}$

$\textbf{g}\bigg)$

$\begin{array}{l} & \dfrac{x^4y^2 - x^2y^4}{x^2(x + y)}(x \ne 0; x \ne -y)
\\ &= \dfrac{x^2y^2 (x^2 - y^2)}{x^2(x + y)}
\\ &= \dfrac{y^2(x + y)(x - y)}{x + y}
\\ &= y^2(x - y)\end{array}$