Question

giải phương trình sau: x/(x-2) 1=(2x2 3)/x2-4 

Answer 1

ĐKXĐ: \(x\notin\left\{2;-2\right\}\)

Ta có: \(\dfrac{x}{x-2}+1=\dfrac{2x^2+3}{x^2-4}\)

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

Suy ra: \(x^2+2x+x^2-4=2x^2+3\)

\(\Leftrightarrow2x-4=3\)

\(\Leftrightarrow2x=7\)

\(\Leftrightarrow x=\dfrac{7}{2}\)(thỏa ĐK)

Vậy: \(S=\left\{\dfrac{7}{2}\right\}\)