Question

Помогите пожалуйста решить примеры по алгебре

Answer 1

Ответ:

$1)\;\; \frac{3x}{y}+\frac{6}{x}=\frac{3x^2+6y}{xy}=\frac{3(x^2+2y)}{xy}\\\\2)\;\;\frac{5}{x}-\frac{3}{x+y}=\frac{5x+5y-3x}{x(x+y)}=\frac{5(x+y)-3x}{x(x+y)}\\\\3)\;\;\frac{5x}{2y}:\frac{10x^2}{4y}=\frac{5x}{2y}*\frac{4y}{10x^2}=\frac{1}{x}\\\\4)\;\;\frac{5a^2}{1-a^2}:(1-\frac{1}{1+a})=\frac{5a^2}{(1+a)(1-a)}:\frac{1+a-1}{(1+a)}=\frac{5a^2}{(1+a)(1-a)}*\frac{(1+a)}{a} = \frac{5a}{1-a}$

$5)\;\;\frac{x^2-4}{a^2-9}:\frac{x^2-2x}{ay+3y}+\frac{2-y}{a-3}=\frac{(x+2)(x-2)}{(a+3)(a-3)}*\frac{y(a+3)}{x(x-2)} +\frac{2-y}{a-3}=\frac{xy+2y}{x(a-3)}+\frac{2-y}{a-3} = \\\\=\frac{xy+2y+2x-xy}{x(a-3)}=\frac{2(y+x)}{x(a-3)}$