Question

x-y_ 5y
->
5y
a)*
x²-xy
5y
х
x2

Answer 1

Ответ:

Применяем формулы сокращённого умножения .

$\displaystyle a)\ \ \frac{x-y}{x}-\frac{5y}{x^2}\cdot \frac{x^2-xy}{5y}=\frac{x-y}{x}-\frac{x(x-y)}{x^2}=\frac{x-y}{x}-\frac{x-y}{x}=0$  

$\displaystyle b)\ \ \Big(\frac{a}{b^2-ab}+\frac{b}{a^2-ab}\Big)\cdot \frac{ab}{b-a}= \Big(\frac{a}{b(b-a)}+\frac{b}{a(a-b)}\Big)\cdot \frac{ab}{b-a}=\\\\\\=\Big(\frac{a}{b(b-a)}-\frac{b}{a(b-a)}\Big)\cdot \frac{ab}{b-a}=\frac{a^2-b^2}{ab(b-a)}\cdot \frac{ab}{b-a}=\frac{(a-b)(a+b)}{ab(b-a)^2}=\\\\\\=\frac{(a-b)(a+b)}{ab(a-b)^2}=\frac{a+b}{ab(a-b)}$