Question

$(frac{2ab}{a^2-b^2}+frac{a-b}{2a+2b})*frac{2a}{a+b}+frac{b}{b-a}$

Answer 1

$(frac{2ab}{a^2-b^2}+frac{a-b}{2a+2b})*frac{2a}{a+b}+frac{b}{b-a}=frac{5b-a}{4b-4a}\ 1) frac{2ab}{a^2-b^2}+frac{a-b}{2a+2b}=frac{2ab}{(a-b)(a+b)}+frac{a-b}{2(a+b)}=frac{4ab+a^2-2ab+b^2}{2(a^2-b^2)}=frac{(a+b)^2}{2(a^2-b^2)}\ 2)frac{(a+b)^2}{2(a^2-b^2)}*frac{2a}{a+b}=frac{(a+b)(a+b)*2a}{2(a-b)(a+b)(a+b)}=frac{a}{a-b}\3)frac{a}{a-b}+frac{b}{b-a}=frac{a}{a-b}-frac{b}{a-b}=frac{a-b}{a-b}=1$

Answer 2

1) 2ab             a-b          2ab                     a-b             4ab+(a-b)^2          4ab+a^2-2ab+b^2

  -----------  +---------- = --------------  + -----------      = ------------------  =  ---------------------------  =

  a^2-b^2       2a+2b     (a-b)(a+b)        2(a+b)         2 (a-b)(a+b)                2(a-b)(a+b)

 

     2ab+a^2+b^2             (a+b)^2                 a+b

= ---------------------  = --------------------  = ------------

        2(a-b)(a+b)            2(a-b)(a+b)         2(a-b)

 

2)   a+b              2a           (a+b) * 2a            a

     --------   *  ---------  = ------------------- = ----------

      2(a-b)        (a+b)        2(a-b) (a+b)        a-b

 

3) a         b               a              b            a-b

  ----- +---------  = ---------  - ---------  = --------  = 1

   a-b        b-a         a-b         a-b            a-b

Ответ:1