161.

Zadatak

TEKST ZADATKA

Srediti izraz:

ax+2x−2x3−x−1x−ax2−1\frac{ax+2x-2}{x^3-x}-\frac{1}{x}-\frac{a}{x^2-1}
REŠENJE ZADATKA

Sređuju se razlomci:

ax+2x−2x(x2−1)−1x−ax2−1=ax+2x−2−(x2−1)−axx(x2−1)\frac{ax+2x-2}{x(x^2-1)}-\frac{1}{x}-\frac{a}{x^2-1}=\frac{\cancel{ax}+2x-2-(x^2-1)-\cancel{ax}}{x(x^2-1)}
ax+2x−2−(x2−1)−axx(x2−1)=−x2−1+2xx(x2−1)\frac{\cancel{ax}+2x-2-(x^2-1)-\cancel{ax}}{x(x^2-1)}=\frac{-x^2-1+2x}{x(x^2-1)}

Primenjuje se formula za razliku kvadrata:a2−b2=(a−b)(a+b)a^2-b^2=(a-b)(a+b)

−x2−2x+1x(x−1)(x+1)-\frac{x^2-2x+1}{x(x-1)(x+1)}

Primenjuje se formula za kvadrat razlike: (a−b)2=a2−2ab+b2(a-b)^2=a^2-2ab+b^2

−(x−1)2x(x−1)(x+1)=−x−1x(x+1)-\frac{(x-1)^{\cancel{2}}}{x\cancel{(x-1)}(x+1)}=-\frac{x-1}{x(x+1)}

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