Question

[Thanh Thanh]

giải pt:

giúp mk vs ạ mk cần gấp

Answer 1

[Nguyễn Việt Lâm]

ĐKXĐ: \(x\ne\left\{2;\dfrac{1}{2};3\right\}\)

\(\dfrac{x+4}{2x^2-5x+2}+\dfrac{x+1}{2x^2-7x+3}=\dfrac{2x+5}{2x^2-7x+3}\)

\(\Leftrightarrow\dfrac{x+4}{2x^2-5x+2}-\dfrac{2x+5}{2x^2-7x+3}+\dfrac{x+1}{2x^2-7x+3}=0\)

\(\Leftrightarrow\dfrac{x+4}{2x^2-5x+2}-\dfrac{x+4}{2x^2-7x+3}=0\)

\(\Leftrightarrow\left(x+4\right)\left(\dfrac{1}{2x^2-5x+2}-\dfrac{1}{2x^2-7x+3}\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x+4=0\\2x^2-5x+2=2x^2-7x+3\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-4\\x=\dfrac{1}{2}\left(loại\right)\end{matrix}\right.\)