Question

\(\dfrac{x-2}{x+2}\)-\(\dfrac{3}{x-2}\)=\(\dfrac{2\times\left(x-11\right)}{x^2-4}\)

Answer 1

DKXD:x\(\ne\)\(\pm\)2

\(\dfrac{x-2}{x+2}-\dfrac{3}{x-2}=\dfrac{2\left(x-11\right)}{x^2-4}\Leftrightarrow\dfrac{\left(x-2\right)^2-3\left(x+2\right)}{\left(x+2\right)\left(x-2\right)}=\dfrac{2x-22}{\left(x+2\right)\left(x-2\right)}\)

\(\Rightarrow\)x²-4x+4-3x-6=2x-22\(\Leftrightarrow\)x²-4x-3x-2x+22+4-6=0\(\Leftrightarrow\)x²-9x+20=0

\(\Leftrightarrow\)(x-4)(x-5)\(\Leftrightarrow\left\{{}\begin{matrix}x-4=0\Leftrightarrow x=4\left(TM\right)\\x-5=0\Leftrightarrow x=5\left(TM\right)\end{matrix}\right.\)

Vậy tập nghiệm của PT là:S={4;5}