Question

\(gpt:x^2+\frac{4x^2}{\left(x+2\right)^2}=5\)

Answer 1

\(ĐKXĐ:x\ne-2\)

\(Pt\Leftrightarrow x^2+4x+4+\frac{4x^2}{\left(x+2\right)^2}-4x=9\)

   \(\Leftrightarrow\left(x+2\right)^2-4x+\frac{4x^2}{\left(x+2\right)^2}=9\)

  \(\Leftrightarrow\left(x+2-\frac{2x}{x+2}\right)^2=9\)

  \(\Leftrightarrow x+2-\frac{2x}{x+2}=\pm3\)

*Với \(x+2-\frac{2x}{x+2}=3\)

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

\(\Leftrightarrow x^2+2x+4=3x+6\)

\(\Leftrightarrow x^2-x-2=0\)

\(\Leftrightarrow\left(x+1\right)\left(x-2\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x=-1\\x=2\end{cases}}\)(Tm ĐKXĐ)

trường hợp còn lại làm tương tự nhé!