a/ $35x+45.\bigg(x-\dfrac{2}{5}\bigg)=90$
$↔35x+45x-18=90$
$↔80x=108$
$↔x=\dfrac{27}{20}$
Vậy $S=\bigg\{\dfrac{27}{20}\bigg\}$
b/ $\dfrac{x}{40}=\dfrac{x}{50}+\dfrac{3}{4}$
$↔\dfrac{5x}{200}-\dfrac{4x}{200}=\dfrac{3}{4}$
$↔\dfrac{x}{200}=\dfrac{3}{4}$
$↔x=150$
Vậy $S=\{150\}$
c/ $\dfrac{x}{60}-\dfrac{x}{80}=1$
$↔\dfrac{8x}{480}-\dfrac{6x}{480}=1$
$↔\dfrac{2x}{480}=1$
$↔2x=480$
$↔x=240$
vậy $S=\{240\}$
d/ $\dfrac{120}{x}-\dfrac{120}{x+10}=\dfrac{2}{5}$ ($x\ne 0;-10$)
$↔\dfrac{120(x+10)-120x}{x(x+10)}=\dfrac{2}{5}$
$↔\dfrac{1200}{x(x+10)}=\dfrac{2}{5}$
$↔2x(x+10)=6000$
$↔2x²+20x-6000=0$
$↔x²+10x-3000=0$
$↔x²+10x+25-3025=0$
$↔(x+5)²-3025=0$
$↔(x-50)(x+60)=0$
$↔x-50=0\quad or\quad x+60=0$
$↔x=50(TM)\quad or\quad x=-60(KTM)$
Vậy $S=\{50;-60\}$
