Question

Упростите выражение

$frac{x-5}{x^2+5x}+frac{x+5}{x^2-5x} - frac{4x}{x^2-25}$

Answer 1

$frac{x-5}{x^2+5x} +frac{x+5}{x^2-5x}-frac{4x}{x^2-25}= frac{(x-5)^2+(x+5)^2}{x(x-5)(x+5)}- frac{4x}{x^2-25}=$
$= frac{x^2-10x+25+x^2+10x+25}{x(x^2-25)}- frac{4x^2}{x(x^2-25)}= frac{2x^2+50-4x^2}{x(x^2-25)} =$
$frac{50-2x^2}{x(x^2-25)} = frac{2(25-x^2)}{x(x^2-25)}=- frac{2}{x}$