Question

(x-1) (5x+3)=(3x-8) (x-1)

Answer 1

\(\frac{x-1}{5x+3}=\frac{3x-8}{x-1}\left(ĐKXĐ:x\ne\frac{-3}{5},x\ne1\right)\)

\(\Leftrightarrow\frac{\left(x-1\right)^2-\left(5x+3\right)\left(3x-8\right)}{\left(5x+3\right)\left(x-1\right)}\)

\(\Leftrightarrow x^2-2x+1-15x^2+31x+24=0\)

\(\Leftrightarrow-14x^2+29x+25=0\)

Pt nghiệm vô tỉ

Answer 2

Ta có: (x-1)(5x+3)=(3x-8)(x-1)

⇔(x-1)(5x+3)-(3x-8)(x-1)=0

⇔(x-1)(5x+3-3x+8)=0

hay (x-1)(2x+11)=0

⇔\(\left[{}\begin{matrix}x-1=0\\2x+11=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\2x=-11\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=\frac{-11}{2}\end{matrix}\right.\)

Vậy: \(x\in\left\{1;\frac{-11}{2}\right\}\)