Question

Помогите с примерами!!!!

Answer 1

$1) \frac{b(a+b)^2}{a^4-b^4} + \frac{a}{a^2+b^2} =\\ = \frac{a^2b + 2ab^2 + b^3 + a^3 - ab^2}{a^4-b^4} =\\ = \frac{a^2b + ab^2 + b^3 + a^3}{(a-b)(a^3 + a^2b+ab^2+b^3)}=\\ = \frac{1}{a-b}$

$2) \frac{x+40}{x(x-4)(x+4)} :( \frac{x-4}{(3x-1)(x+4)}- \frac{16}{(4+x)(4-x)} )=\\ = \frac{x+40}{x(x-4)(x+4)} :( \frac{8x-x^2-16}{(3x-1)(x+4)(4-x)}- \frac{48x-16}{(4+x)(4-x)(3x-1)} )=\\ = \frac{x+40}{x(x-4)(x+4)} :( \frac{-x(40+x)}{(3x-1)(x+4)(4-x)} )=\\ =\frac{x+40}{x(x-4)(x+4)} *( \frac{(3x-1)(x+4)(4-x)}{-x(x+40)} )=\\ = \frac{3x-1}{x^2}$