Question

Tìm x; biết: 

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

Answer 1

x + 1/x = x - 2/x - 1

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

=> (x + 1).x - (x + 1) = x² - 2.x

=> x² + x - x - 1 = x² - 2.x

=> x² - 1 = x² - 2.x

=> 1 = 2.x

=> x = 1/2

Answer 2

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

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

\(x^2+x-x-1=x^2-2x\)

\(2x=1\)

\(x=\frac{1}{2}\)