Сократите дробь: [latex] \frac{x^4-y^4}{x^3+xy^2-x^2y-y^3} [/latex]

Question

Сократите дробь: [latex] \frac{x^4-y^4}{x^3+xy^2-x^2y-y^3} [/latex]

Алгебра

Гость

Ответ(ы) на вопрос:

Accepted Answer

[latex] \frac{x^4-y^4}{x^3+xy^2-x^2y-y^3}= \frac{(x^2-y^2)(x^2+y^2)}{(x^3-x^2y)+(xy^2-y^3)}= \frac{(x^2-y^2)(x^2+y^2)}{x^2(x-y)+y^2(x-y)}= [/latex] [latex]=\frac{(x^2-y^2)(x^2+y^2)}{(x-y)(x^2+y^2)}= \frac{x^2-y^2}{x-y} = \frac{(x-y)(x+y)}{x-y} =x+y[/latex]