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Treść w załączniku

Treść W Załączniku class=

Odpowiedź :

Wik8947201viz

[tex]\\(\frac{x}{x-y}-\frac{2xy}{x^2-y^2}+\frac{x}{x+y}):\frac{2xy}{x+y}= \\\frac{x(x+y)-2xy+x(x-y)}{x^2-y^2}*\frac{x+y}{2x}= \\\frac{x^2+xy-2xy+x^2-xy}{(x+y)(x-y)}*\frac{x+y}{2x}= \\\frac{2x^2-2xy}{x-y}*\frac{1}{2x}=\frac{2x(x-y)}{x-y}*\frac{1}{2x}=1 \\c.n.d.[/tex]

 

Basetlaviz

    x               2xy                x                  2x

(-------   -   -----------   +   ---------)  :  (---------)   =

  x - y          x² - y²            x + y           x + y

 

x(x + y) - 2xy + x(x - y)           2x(x - y)

------------------------------   :   -----------------   =  

    (x + y)(x - y)                     (x + y)(x - y)

 

x² + xy - 2xy + x² - xy            2x² - 2xy

----------------------------   :   ------------------   =

    (x + y)(x - y)                   (x + y)(x - y)

 

   2x² - 2xy              (x + y)(x - y)

-----------------   *   --------------------   =   1

(x + y)(x - y)             2x² - 2xy

 

c.n.d.

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