Question

$\frac{15}{x} -\frac{15}{x+12}=4$
Решите. Дам 44 балла.

Answer 1

15/x - 15/(x+12) = 4
ОДЗ x≠0 x≠-12
15*(1/x - 1/(x+12)) = 4
15*( (x+12)/x(x+12) - x/(x+12)x ) = 4
15*(x+12-x)/x(x+12) = 4
15*12 = 4(x+12)x
45 = x^2 + 12x
x^2+12x-45=0
D=144+180=324=18^2
x12=(-12+-18)/2 = -15 3
ответ -15 и 3

Answer 2

$\frac{15*(x+12)-15x}{ x^{2} +12x} =4 \\ \\ \frac{15x+180-15x}{ x^{2} +12x} =4 \\ \\ \frac{180}{ x^{2} +12x} =4 \\ \\ 4*( x^{2} +12x)=180 \\ 4 x^{2} +48x=180 \\ x^{2} +12x=45 \\ x^{2} +12x-45=0 \\ D= 12^{2} -4*(-45)=144+180= \sqrt{324} =18 \\ x_{1} = \frac{-12-18}{2} = \frac{-30}{2} =-15 \\ x_{2} = \frac{-12+18}{2} = \frac{6}{2} =3$

ответ: -15 ; 3