Question

1．解方程组：$\left\{\begin{array}{l}\frac{4}{x+y}+\frac{6}{x-y}=3\\ \frac{9}{x-y}-\frac{1}{x+y}=1\end{array}\right.$．

Answer 1

分析 方程组换元整理后，利用加减消元法求出解即可．

解答 解：设$\frac{1}{x+y}$=u，$\frac{1}{x-y}$=v，
方程组整理得：$\left\{\begin{array}{l}{4u+6v=3①}\\{9v-u=1②}\end{array}\right.$，
①+②×4得：42v=7，即v=$\frac{1}{6}$，
把v=$\frac{1}{6}$代入①得：u=$\frac{1}{2}$，
∴$\left\{\begin{array}{l}{\frac{1}{x+y}=\frac{1}{2}}\\{\frac{1}{x-y}=\frac{1}{6}}\end{array}\right.$，即$\left\{\begin{array}{l}{x+y=2}\\{x-y=6}\end{array}\right.$，
解得：$\left\{\begin{array}{l}{x=4}\\{y=-2}\end{array}\right.$，
经检验$\left\{\begin{array}{l}{x=4}\\{y=-2}\end{array}\right.$是方程组的解．

点评 此题考查了解二元一次方程组，利用了换元的思想，熟练掌握运算法则是解本题的关键．