Question

Va rog ajutati-ma sa simplific raportul :
$(\frac{x}{y} - \frac{y}{x} ) * \frac{5xy}{x-y}$

Answer 1

   
[tex]\displaystyle\\ \Big (\frac{x}{y} - \frac{y}{x}\Big) \cdot \frac{5xy}{x-y} =\\\\ =\Big (\frac{x\cdot x}{y\cdot x} - \frac{y\cdot y}{x\cdot y}\Big) \cdot \frac{5xy}{x-y} =\\\\ =\Big (\frac{x^2}{xy} - \frac{y^2}{xy}\Big)\cdot \frac{5xy}{x-y} =\\\\ =\frac{x^2-y^2}{xy}\cdot \frac{5xy}{x-y} =\\\\ =\frac{(x+y)(x-y)}{xy}\cdot \frac{5xy}{x-y} =\\\\ =\frac{5xy(x+y)(x-y)}{xy(x-y)}= \boxed{\bf 5(x+y)} [/tex]

Answer 2

[tex]\frac{x^2-y^2}{xy} \cdot \frac{5xy}{x-y}=\\ \frac{(x-y)(x+y)}{xy}\cdot \frac{5xy}{x-y}=5(x+y)\\ [/tex]