Question

решите уравнение
$\frac{x}{x + 5} - \frac{x - 2}{x + 21} = \frac{1}{3}$
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Answer 1

$\frac{x}{x+5}-\frac{x-2}{x+21}=\frac{1}{3}\\\\\frac{x^{2}+21x-x^{2}+2x-5x+10}{(x+5)(x+21)}=\frac{1}{3}\\\\\frac{18x+10}{(x+5)(x+21)}=\frac{1}{3} \\\\\left \{ {{(x+5)(x+21)=54x+30} \atop {x\neq-5;x\neq-21}} \right.$

$(x+5)(x+21)=54x+30\\\\x^{2}+21x+5x+105-54x-30=0\\\\x^{2}-28x+75=0\\\\D=(-28)^{2}-4*75=784-300=484=22^{2}\\\\x_{1} =\frac{28+22}{2}=25\\\\x_{2}=\frac{28-22}{2}=3\\\\Otvet:\boxed{3;25}$