Explicație pas cu pas:
Folosim formula (ax ± b)² = a²x² ± 2abx + b²
Dacă a = 1, formula devine: (x ± b)² = x² ± 2bx + b²
a)
[tex]\frac{x^{2}+2x+1 }{3x^{5} +3x^{4} } *\frac{x^{5} }{x-1} =\frac{(x+1)^{2}}{3x^{4} (x+1) } *\frac{x^{5} }{x-1}=\frac{x+1}{3} *\frac{x}{x-1}=\frac{x(x+1)}{3(x-1)} =\frac{x^{2} +x}{3x-3}[/tex]
b)
[tex]\frac{x^{2} -4x+4}{x+5} *\frac{x^{3}}{2x^{2} -4x} =\frac{(x -2)^{2} }{x+5} *\frac{x^{3}}{2x(x-2)}=\frac{x -2}{x+5} *\frac{x^{2}}{2}=\frac{x^{2} (x-2)}{2(x+5)} =\frac{x^{3}-2 x^{2}}{2x+10}[/tex]
