Question

Rút gọn biểu thức :

\(B=\dfrac{2}{xy}\div\left(\dfrac{1}{x}-\dfrac{1}{y}\right)^2-\dfrac{x^2+y^2}{\left(x-y\right)^2}\)

Answer 1

\(B=\dfrac{2}{xy}\div\left(\dfrac{1}{x}-\dfrac{1}{y}\right)^2-\dfrac{x^2+y^2}{\left(x-y\right)^2}\)

\(B=\dfrac{2}{xy}\div\left(\dfrac{y-x}{xy}\right)^2-\dfrac{x^2+y^2}{\left(x-y\right)^2}\)

\(B=\dfrac{2}{xy}\div\dfrac{\left(y-x\right)^2}{\left(xy\right)^2}-\dfrac{x^2+y^2}{\left(x-y\right)^2}\)

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

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

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

\(B=\dfrac{2xy-x^2-y^2}{\left(x-y\right)^2}\)

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

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

Answer 2

\(B=\dfrac{2}{xy}:\left(\dfrac{1}{x}-\dfrac{1}{y}\right)^2-\dfrac{x^2+y^2}{\left(x-y\right)^2}\)

\(=\dfrac{2xy}{\left(x-y\right)^2}-\dfrac{x^2+y^2}{\left(x-y\right)^2}=\dfrac{-\left(x-y\right)^2}{\left(x-y\right)^2}=-1\)