Question

Решите уравнение 
$frac{800}{x-5} *(x-1)- frac{720}{x-1} *(x-5)=360$

Answer 1

 
 $frac{800}{x-5} (x-1) - frac{720(x-5)}{x-1} = 360\\ x-5=a\ x-1=b\\ frac{800b}{a} - frac{ 720 a}{b} = 360 \ 800b^2-720a^2 = 360ab\ 40(4b+3a)(5b-6a) = 0\ 4x-4=-3x+15\ 7x=19\ x=frac{19}{7}\\ 5x-5=6x-30\ x=25$

Answer 2

$frac{800(x-1)}{x-5}-frac{720(x-5)}{x-1}=360\ \ x neq 5, x neq 1\ \ frac{800(x-1)^2-720(x-5)^2}{(x-5)(x-1)}=360\ \ 800(x^2-2x+1)-720(x^2-10x+25)=360(x-5)(x-1)\ 800x^2-1600x+800-720x^2+7200x-18000=360(x^2-6x+5)\ 80x^2+5600x-17200-360x^2+2160x-1800=0\ 280x^2-7760x+19000=0 |:40\ 7x^2-194x+475=0\ D=37636-4*7*475=37636-13300=24336=156^2\ x_1=frac{194+156}{14}=25\ x_2=frac{194-156}{14}=frac{19}{7}$
Ответ:  25, 19/7