Question

Помогите!Решить:
1)a²+2ab+b²/ a²-ab+b² : 8a-8b/ a³+b³
2)n³-m³/ n²-m² : n²+nm+m²/ n²+2nm+m²

Answer 1

$\frac{a^2-2ab+b^2}{a^2-ab+b^2}: \frac{8a-8b}{a^3+b^3}= \frac{(a-b)^2}{a^2-ab+b^2}* \frac{(a+b)(a^2-ab+b^2)}{8(a-b)}= \frac{(a-b)(a+b)}{8}= \frac{a^2-b^2}{8} \\ \\ \frac{n^3-m^3}{n^2-m^2}: \frac{n^2+nm+m^2}{n^2+2nm+m^2}= \frac{(n-m)(n^2+nm+m^2)}{(n-m)(n+m)}* \frac{(n+m)^2}{n^2+nm+m^2}= \\ = \frac{n^2+nm+m^2}{n+m}* \frac{(n+m)^2}{n^2+nm+m^2}= \frac{(n+m)^2}{n+m}=n+m$