Question

\(\dfrac{x+2}{x-2}+\dfrac{1}{2}=\dfrac{-2}{x\left(x-2\right)}\)

4(3x-2)=3x+1

Answer 1

\(\dfrac{x+2}{x-2}\) + \(\dfrac{1}{2}\)  = \(\dfrac{-2}{x\left(x-2\right)}\) (1)

ĐKXĐ \(\Leftrightarrow\) x - 2 \(\ne\) 0 \(\Leftrightarrow\) x \(\ne\) 2

(1) \(\dfrac{2x\left(x+2\right)}{2x\left(x-2\right)}\)  + \(\dfrac{x\left(x-2\right)}{2x\left(x-2\right)}\)  = \(\dfrac{\left(-2\right)2}{2x\left(x-2\right)}\) 

\(\Leftrightarrow\) 2x(x + 2) + x(x - 2) = (-2)2

\(\Leftrightarrow\) 2x² + 4x + x² - 2x = -4

\(\Leftrightarrow\) 2x² + 4x + x² - 2x + 4 = 0

\(\Leftrightarrow\) 3x² + 2x + 4 = 0 (vô lý)

Pt này vô nghiệm nha

4(3x - 2) = 3x + 1

12x - 8 = 3x + 1

12x - 8 - 3x - 1 = 0

9x - 9 = 0 

        x = 1

S =\(\left\{1\right\}\)