Đáp án:
a) $\dfrac{2x+3}{5x+2}$ = $\dfrac{4x+5}{10x+1}$
ĐKXĐ : x $\neq$ -$\dfrac{2}{5}$ ; x $\neq$ -$\dfrac{1}{10}$
⇔ $\dfrac{(2x+3)(10x+1)}{(5x+2)(10x+1)}$ = $\dfrac{(4x+5)(5x+2)}{(10x+1)(5x+2)}$
⇒ (2x+3)(10x+1) = (4x+5)(5x+2)
⇔ 20x² + 2x + 30x + 3 = 20x² + 8x + 25x + 10
⇔ 20x² - 20x² + 2x +30x - 8x -25x= 10 - 3
⇔ -x= 7
⇔ x= 7 : (-1)
⇔ x = -7 (thỏa mãn)
Vậy x = -7
b) $\dfrac{3x-1}{40-5x}$ = $\dfrac{25-3x}{5x-34}$
ĐKXĐ : x $\neq$8 ; x $\neq$ $\dfrac{34}{5}$
⇔ $\dfrac{(3x-1)(5x-34)}{(40-5x)(5x-34)}$ = $\dfrac{(25-3x)(40-5x)}{(5x-34)(40-5x)}$
⇒ (3x-1)(5x-34) = (25-3x)(40-5x)
⇔ 15x² - 102x - 5x + 34 = 1000 - 125x - 120x + 15x²
⇔ 15² - 15x² -102x - 5x+125x + 120x = 1000 -34
⇔ 138x = 966
⇔ x = 966 : 138
⇔ x = 7 (TM)
Vậy x = 7
c) x : 2 = y:5 và x+y = 21
Theo đề , ta có :
$\dfrac{x}{2}$ = $\dfrac{y}{5}$
⇒ $\dfrac{x+y}{2+5}$ = $\dfrac{21}{7}$= 3
⇒ x = 3 . 2 = 6
⇒ y = 3 . 5 = 15
