Løs likning ved regning

[Trond]

[tex]\frac{2}{x} - \frac{2}{{x + 1}} = 1[/tex]


Fasit er: x = -2 eller x = 1

[Gjest]

[tex]\frac{2}{x}-\frac{2}{x+1}=1 \\\frac{2(x+1)}{x(x+1)}-\frac{2x}{x(x+1)}=\frac{x(x+1)}{x(x+1)}\\ 2(x+1)-2x = x(x+1) \\ 2x+2-2x=x^2+x\\ 2x+2-2x-x^2-x=0 \\ -x^2-x+2 =0 \\ x^2+x-2=0 \\ (x+2)(x-1)=0\\ \underline{\underline{x = -2 \text{ og } x = 1}}[/tex]