Question

Rút gọn :        \(\frac{2}{xy}:\left(\frac{1}{x}-\frac{1}{y}\right)^2-\frac{x^2+y^2}{\left(x-y\right)^2}\)

Answer 1

\(\frac{2}{xy}:\left(\frac{1}{x}-\frac{1}{y}\right)^2-\frac{x^2+y^2}{\left(x-y\right)^2}\left(ĐK:x\ne0;y\ne0\right)\)

\(=\frac{2}{xy}:\left(\frac{y-x}{xy}\right)^2-\frac{x^2+y^2}{\left(x-y\right)^2}\)

\(=\frac{2}{xy}\cdot\frac{x^2y^2}{\left(y-x\right)^2}-\frac{x^2+y^2}{\left(x-y\right)^2}\)

\(=\frac{-2xy}{\left(x-y\right)^2}+\frac{x^2+y^2}{\left(x-y\right)^2}\)

\(=\frac{-2xy+x^2+y^2}{\left(x-y\right)^2}\)

\(=\frac{\left(x-y\right)^2}{\left(x-y\right)^2}=1\)

 

Answer 2

\(\frac{2}{xy}:\left(\frac{1}{x}-\frac{1}{y}\right)^2-\frac{x^2+y^2}{\left(x-y\right)^2}\left(dk:x\ne y\ne0\right)\)

miik ko nghĩ nó là toán lớp 7 đâu bn