Question

Simplificați rapoartele si apoi efectuați înmulțirile:
$\frac{ {x}^{2} - 4x + 4}{x + 5} \times \frac{ {x}^{3} }{2 {x}^{2} - 4x } =$
DAU COROANA!​

Answer 1

 

$\displaystyle\\~~~~\frac{x^2-4x+4}{x+5}\times\frac{x^3}{2x^2-4x}=\\\\\\=\frac{x^2-2\cdot2x+2^2}{x+5}\times\frac{x^3}{2x(x-2)}=\\\\\\=\frac{(x-2)^2}{x+5}\times\frac{x^2}{2(x-2)}=\\\\\\\text{Simplificam numaratorul primei fractii cu numitoru fractiei a doua cu }x-2\\\\\\=\frac{x-2}{x+5}\times\frac{x^2}{2}=\boxed{\frac{x^2(x-2)}{2(x+5)}}$