Odpowiedź:
2.
a)
[tex]5+\frac{1}{x-1}\\ \frac{5(x-1)+1}{x-1}\\ \frac{5x-5+1}{x-1} \\\frac{5x-4}{x-1}\\[/tex]
b)
[tex]\frac{3x}{x+2} - \frac{x+3}{x}\\ \frac{3x^{2} -(x+2). (x+3)}{x. (x+2)}\\ \frac{3x^{2} -(x^{2} +3x+2x+6)}{x^{2} +2x}\\ \frac{3x^{2} -(x^{2} +5x+6)}{x^{2} +2x}\\ \frac{3x^{2} -x^{2} -5x-6}{x^{2} +2x}\\ \frac{2x^{2} -5x-6}{x^{2} +2x}[/tex]
c)
[tex]\frac{x^{2}+8x }{2x^{2} +16x}:\frac{x^{2}+8x+16 }{2x+8}\\ \frac{x^{2}+8x }{2(x^{2}+8x) }. \frac{x^{2}+8x+16 }{2x+8}\\ \frac{1}{2}. \frac{(x+4)^{2} }{2(x+4)}\\ \frac{1}{2}. \frac{x+4}{2}\\ \frac{x+4}{4}[/tex]
d)
[tex]\frac{9-x^{2} }{27-x^{3} }. \frac{81-x^{2} }{9+x^{2} } \\ \frac{(3-x). (3+x)}{(3-x). (9+3x+x^{2}) } . \frac{81-x^{2} }{9+x^{2} }\\ \frac{3+x}{9+3x+x^{2} }. \frac{81-x^{2} }{9+x^{2} } \\ \frac{(3+x). (81-x^{2} )}{(9+3x+x^{2} ). (9+x^{2} } \\\frac{242=3x^{2} +81x-x^{3} }{81+9x^{2} +27x+3x^{3}+9x^{2} +x^{4} }\\ \frac{-x^{3}-3x^{2} +81+243 }{81+18x^{2} +27x+3x^{3}+x^{4} }\\\\\frac{-x^{3}-3x^{2} +81x+243 }{x^{4}+3x^{3}+18x^{2} +27x+81 } \\[/tex]
Szczegółowe wyjaśnienie:
