Question

помогите
нужно упростить выражения ДАЮ 40 БАЛОВ ​

Answer 1

1)

$\displaystyle\\\frac{\frac{1}{x}+\frac{1}{y}}{\frac{1}{x} -\frac{1}{y}} = \frac{\frac{x+y}{xy}}{\frac{y-x}{xy}}=\frac{x+y}{y-x}$

2)

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

3)

$\displaystyle\\\frac{\frac{1}{x}-\frac{1}{2x}}{\frac{1}{x^2}-\frac{1}{2x^2}}=\frac{\frac{1}{2x}}{\frac{1}{2x^2}}=x$

4)

$\displaystyle\\\frac{a-\frac{x^2}{a}}{x-\frac{a^2}{x}}=\frac{\frac{a^2-x^2}{a}}{\frac{x^2-a^2}{x}}=-\frac{\frac{a^2-x^2}{a}}{\frac{a^2-x^2}{x}}=-\frac{x}{a}$