Question

7. Довести, що значення виразу залежить відзначеної. ​

Answer 1

Ответ:

$1$

Объяснение:

$\displaystyle \left(\frac{x^2}{5-x}+\frac{x^2}{5+x}\right):\frac{10x^2}{x^2-10x+25}+\frac{2x}{x+5}=\\\\\\\left(\frac{-x^2}{x-5}+\frac{x^2}{x+5}\right):\frac{10x^2}{(x-5)^2}+\frac{2x}{x+5}=\\\\\\\left(\frac{-x^2(x+5)}{(x-5)(x+5)}+\frac{x^2(x-5)}{(x-5)(x+5)}\right):\frac{10x^2}{(x-5)^2}+\frac{2x}{x+5}=$

$\displaystyle\frac{-x^2(x+5)+x^2(x-5)}{(x-5)(x+5)}\cdot \frac{(x-5)^2}{10x^2}+\frac{2x}{x+5}=\\\\\\\frac{-x^3-5x^2+x^3-5x^2}{x+5}\cdot \frac{x-5}{10x^2}+\frac{2x}{x+5}=\\\\\\\frac{-10x^2}{x+5}\cdot \frac{x-5}{10x^2}+\frac{2x}{x+5}=\\\\\\\frac{-(x-5)}{x+5}+\frac{2x}{x+5}=\\\\\\\frac{-x+5}{x+5}+\frac{2x}{x+5}=\\\\\\\frac{-x+5+2x}{x+5}=\frac{x+5}{x+5}=1$