`ĐKXĐ:` $\begin{cases}x\ne 0\\y\ne 0\\x-y\ne 0\\x^2\ne 0\\y^2\ne 0\\\end{cases} \to \begin{cases}x, y\ne 0\\ x\ne y\\\end{cases}$
`a)` $\text{Rút gọn:}$
`M=[\frac{1}{x^2}+\frac{1}{y^2}+\frac{2}{x-y}(\frac{1}{x}-\frac{1}{y})]:(\frac{1}{y^2}-\frac{1}{x^2})`
$\\ \to$ `M=[\frac{1}{x^2}+\frac{1}{y^2}+\frac{2}{x-y}(\frac{y-x}{xy})]:\frac{x^2-y^2}{x^2y^2`
$\\ \to$ `M=[\frac{y^2+x^2}{x^2y^2}+\frac{2(y-x)}{xy(x-y)}].\frac{x^2y^2}{(x-y)(x+y)}`
$\\ \to$ `M=\frac{1}{xy}.[\frac{y^2+x^2}{xy}-\frac{2(x-y)}{x-y}].\frac{x^2y^2}{(x-y)(x+y)}`
$\\ \to$ `M=(\frac{y^2+x^2}{xy}-\frac{2}{1}).\frac{xy}{(x-y)(x+y)`
$\\ \to$ `M=\frac{x^2-2xy+y^2}{xy}.\frac{xy}{(x+y)(x-y)`
$\\ \to$ `M=(x-y)^2 .\frac{1}{(x-y)(x+y)}`
$\\ \to$ `M=\frac{x-y}{x+y}`
`b)` $\text{Khi}$ `x=3, y=1` $\text{ta được:}$
`M=\frac{3-1}{3+1}=\frac{1}{2}`
