Răspuns:
a) [tex]\frac{5(x-1)}{2x(x-2)}[/tex]
b) [tex]\frac{7(x+2)}{3x(x+1)}[/tex]
c) [tex]\frac{2x(2x+1)}{3(x+3)}[/tex]
d) [tex]\frac{2x(3x-1)}{5(x+4)}[/tex]
Explicație pas cu pas:
Se folosesc formulele de calcul:
a²-b² = (a-b)(a+b)
a²-2ab+b² = (a-b)²
a²+2ab+b² = (a+b)²
a) [tex]\frac{x^{2}-2x+1 }{x^{2} -4} * \frac{5x+10}{2x^{2} -2x} = \frac{(x-1)^{2}*5(x+2) }{(x-2)(x+2)*2x(x-1)} = \frac{5(x-1)}{2x(x-2)}[/tex]
b) [tex]\frac{x^{2} +4x+4}{x^{2}-1 } * \frac{7x-7}{3x^{2}+6x } = \frac{(x+2)^{2} * 7(x-1)}{(x-1)(x+1)*3x(x+2)} = \frac{7(x+2)}{3x(x+1)}[/tex]
c) [tex]\frac{4x^{2}+4x+1}{x^{2}-9 } * \frac{2x^{2}-6x }{6x+3} = \frac{(2x+1)^{2} *2x(x-3)}{(x-3)(x+3)*3(2x+1)} = \frac{2x(2x+1)}{3(x+3)}[/tex]
d) [tex]\frac{9x^{2}-6x+1 }{x^{2}-16 } * \frac{2x^{2} -8x}{15x-5} = \frac{(3x-1)^{2} * 2x(x-4)}{(x-4)(x+4)*5(3x-1)} = \frac{2x(3x-1)}{5(x+4)}[/tex]
