Question

Помогите с математикой

Answer 1

Решение:

1-ый пример:

$(\frac{m^2-1}{m^2}-\frac{m^2}{m^2-1})\div(\frac{m^2-2}{m^2+1}+1)=\frac{(m^2-1)^2-(m^2)^2}{m^2(m+1)(m-1)}\div\frac{m^2-2+m^2+1}{m^2+1}=\frac{(m^2-1+m^2)(m^2-1-m^2)(m^2+1)}{m^2(m+1)(m-1)(2m^2-1)}=\frac{-(2m^2-1)(m^2+1)}{m^2(m+1)(m-1)(2m^2-1)}=\frac{-(m^2+1)}{m^2(m+1)(m-1)}=-\frac{x^2+1}{x^4-x^2}$

2-ой пример:

$\frac{x^3-y^3}{\sqrt{x}-\sqrt{y}}=\frac{(x-y)(x^2+xy+y)}{\sqrt{x}-\sqrt{y}} \times \frac{\sqrt{x}+\sqrt{y}}{\sqrt{x}+\sqrt{y}}=\frac{(x-y)(x^2+xy+y)(\sqrt{x}+\sqrt{y})}{x-y}=(x^2+xy+y)(\sqrt{x}+\sqrt{y})=x^2\sqrt{x}+x^2\sqrt{y}+xy\sqrt{x}+xy\sqrt{y}+y^2\sqrt{x}+y^2\sqrt{y}$