Odpowiedź i szczegółowe wyjaśnienie:
[tex][(a+\dfrac{ab}{a-b})(\dfrac{ab}{a+b}-a)]:\dfrac{1}{a-b}=\\\\\\=[\dfrac{a^2b}{a+b}-a^2+\dfrac{a^2b^2}{a^2-b^2}-\dfrac{a^2b}{a-b}]\cdot(a-b)=\\\\\\=[\dfrac{a^2b(a-b)}{(a+b)(a-b)}-\dfrac{a^2(a-b)(a+b)}{(a-b)(a+b)}+\dfrac{a^2b^2}{a^2-b^2}-\dfrac{a^2b(a+b)}{(a-b)(a+b)}]\cdot(a-b)=\\\\\\=[\dfrac{a^3b-a^2b^2}{a^2-b^2}-\dfrac{a^2(a^2-b^2)}{a^2-b^2}+\dfrac{a^2b^2}{a^2-b^2}-\dfrac{a^3b+a^2b^2}{a^2-b^2}]\cdot(a-b)=\\\\\\=[\dfrac{a^3b-a^2b^2-a^4-a^2b^2+a^2b^2-a^3b+a^2b^2}{a^2-b^2}]\cdot(a-b)=\\\\\\[/tex]
[tex]=[\dfrac{-a^4}{a^2-b^2}]\cdot(a-b)=\\\\\\=\dfrac{-a^4}{(a-b)(a+b)}\cdot (a-b)=\\\\\\=\dfrac{-a^4}{a+b}[/tex]
Po wykonaniu przekształceń oraz skróceniu wyrażenia możemy podstawić nasz dane:
[tex]a=-1;\ b=\frac12\\\\\dfrac{-a^4}{a+b}=\dfrac{-(-1)^4}{-1+\frac12}=\dfrac{-1}{-\frac12}=-1\cdot(-2)=2[/tex]
