1.4 Lösning 8b
Från Mathonline
Version från den 5 mars 2011 kl. 17.04 av Taifun (Diskussion | bidrag)
\( {1-x \over x+1} - {1+x \over 1-x} + {4\,x \over 1-x^2} \; = \; {1-x \over 1+x} - {1+x \over 1-x} + {4\,x \over (1+x)\cdot(1-x)} \; = \; \)
\( = \; {(1-x)\cdot(1-x) \over (1+x)\cdot(1-x)} - {(1+x)\cdot(1+x) \over (1-x)\cdot(1+x)} + {4\,x \over (1+x)\cdot(1-x)} \; = \; \)
\( = {(1-x)^2 - (1+x)^2 + 4\,x \over (1+x)\cdot(1-x)} = {1-2\,x+x^2 - (1+2\,x+x^2) + 4\,x \over (1+x)\cdot(1-x)} = \)
\( = {1- 2x + x^2 - 1 - 2x - x^2 + 4x \over (1+x)\cdot(1-x)} = {- 4x + 4x \over (1+x)\cdot(1-x)} = {0 \over (1+x)\cdot(1-x)} = 0 \)
