Question

tìm x biết:

2x-1/3x+2=3x-3/5x-2

giải theo cách tỉ lệ thức nha, bạn nào giải nhanh mình sẽ cho 3 like lun

Answer 1

\(\frac{2x-1}{3x+2}=\frac{3x-3}{5x-2}\)

\(\Rightarrow\left(2x-1\right).\left(5x-2\right)=\left(3x-3\right).\left(3x+2\right)\)

=> (2x - 1).5x - (2x - 1).2 = (3x - 3).3x + (3x - 3).2

=> (10x² - 5x) - (4x - 2) = (9x² - 9x) + (6x - 6)

=> 10x² - 5x - 4x + 2 = 9x² - 9x + 6x - 6

=> 10x² - 9x + 2 = 9x² - 3x - 6

=> 10x² - 9x - 9x² + 3x = -6 - 2

=> x² - 6x = -8

=> x² - 6x + 8 = 0

=> x² - 4x - 2x + 8 = 0

=> x.(x - 4) - 2.(x - 4) = 0

=> (x - 4).(x - 2) = 0

\(\Rightarrow\left[\begin{array}{nghiempt}x-4=0\\x-2=0\end{array}\right.\)\(\Rightarrow\left[\begin{array}{nghiempt}x=4\\x=2\end{array}\right.\)

Vậy \(x\in\left\{2;4\right\}\)

Answer 2

​​\(\frac{2x-1}{3x+2}=\frac{3x-3}{5x-2}=\frac{2x-1-3x+3}{3x+2-5x+2}=\frac{-x+2}{-2x+4}=\frac{x+2}{2x+4}=\frac{x+2}{2.\left(x+2\right)}=\frac{1}{2}\)

\(\frac{2x-1}{3x+2}=\frac{1}{2}\Rightarrow4x-2=3x+2\Rightarrow4x-3x=2+2\Rightarrow x=4\)