Question

Решите уравнение
1/(2х-40)+1/234=1/х

Answer 1

1/2(x-20)+1/234-1/x=0
117x+x*(x-20)-234(x-20)/234x*(x-20)=0
117+x^2-20x-234x+4680/234x*(x-20)=0
-137x+x^2+4680/234x*(x-20)=0
x^2-137x+4680=0
x^2-65x-72x+4680=0
x(x-67)*(x-72)=0
x-65=0
x-72=0
x1=65
x2=72

Answer 2

Ответ:

$x_1=65\\x_2=72$

Пошаговое объяснение:

ОДЗ: x ≠ 20, x ≠ 0

$\frac{1}{2x-40}+\frac{1}{234}=\frac{1}{x}\\\frac{1}{2x-40}+\frac{1}{234}-\frac{1}{x}=0\\\frac{1}{2(x-20)}+\frac{1}{234}-\frac{1}{x}=0\\\frac{117x+x(x-20)-234(x-20)}{234x(x-20)}=0\\\frac{117x+x^2-20x-234x+5680}{234x(x-20)}=0\\\frac{-137x+x^2+4680}{234x(x-20)}=0\\-137x+x^2+4680=0\\x^2-137x+4680=0\\x^2-65x-72x+4680=0\\x(x-65)-72(x-65)=0\\(x-65)(x-72)=0\\x-65=0\\x_1=65\\x-72=0\\x_2=72$