13)
[tex]\dfrac{x^3}{1+x+x^2+x^3} = x^3\cdot \dfrac{1}{x^3+x^2+x+1} = \\ \\ =\dfrac{1}{\dfrac{1}{x^3}} \cdot \dfrac{1}{x^3+x^2+x+1} = \dfrac{1}{\dfrac{x^3+x^2+x+1}{x^3}} =\\ \\= \dfrac{1}{1+\dfrac{1}{x}+\dfrac{1}{x^2}+\dfrac{1}{x^3}}[/tex]
12)
(desfac parantezele)
xy²z³ - xyz + x³yz² - xyz + x²y³z - xyz = 0
(xyz)yz² - 1 + (xyz)x²z - 1 + (xyx)xy² - 1 = 0
yz² - 1 + x²z - 1 + xy² - 1 = 0
=> xy² + yz² + zx² = 1+1+1
=> xy² + yz² + zx² = 3
