Question

Решите уравнение))))
10/x+4/(x-3)=1

Answer 1

$frac{10}{x} + frac{4}{x-3} =1 \ \ 10(x-3)+4x=x(x-3) \ 10x-30+4x= x^{2} -3x \ 14x-30= x^{2} -3x \ x^{2} -3x-14x+30=0 \ x^{2} -17x+30=0 \ \ D=289-120=169 \ sqrt{D} =13 \ x1= frac{17+13}{2} =15 \ x2= frac{17-13}{2} =2 \ \ x neq 0 \ x neq 3$

Ответ:х=15;х=2.

Answer 2

$frac{10}{x}+frac{4}{x-3}=1; xneq0 wedge x-3neq0to xneq0 wedge xneq3\\frac{10(x-3)}{x(x-3)}+frac{4x}{x(x-3)}=1\\frac{10x-30+4x}{x^2-3x}=1\\frac{14x-30}{x^2-3x}=1iff14x-30=x^2-3x\\x^2-3x-14x+30=0\\x^2-17x+30=0$

$x^2-2x-15x+30=0\\x(x-2)-15(x-2)=0\\(x-2)(x-15)=0iff x-2=0 vee x-15=0\\x=2 vee x=15$