Question

Решить уравнение :
$\frac{x - 1}{x + 2} - \frac{x - 2}{x + 3} = \frac{x - 4}{x + 5} - \frac{x - 5}{x + 6}$
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Answer 1

$\frac{x-1}{x+2}-\frac{x-2}{x+3} =\frac{x-4}{x+5}-\frac{x-5}{x+6}\\\\\frac{x^{2}+3x-x-3-x^{2}+4}{(x+2)(x+3)}=\frac{x^{2}+6x-4x-24-x^{2}+25}{(x+5)(x+6)}\\\\\frac{2x+1}{(x+2)(x+3)} =\frac{2x+1}{(x+5)(x+6)}\\\\1)(x+2)(x+3)=(x+5)(x+6)\\\\x^{2} +5x+6=x^{2} +11x+30\\\\11x-5x=6-30\\\\6x=-24\\\\\boxed{x=-4}$

$2)2x+1=0\\\\2x=-1\\\\\boxed{x=-0,5}\\\\Otvet:\boxed{-4 \ ; \ -0,5}$