Question

\(x.\frac{8-x}{x-1}\left(x-\frac{8-x}{x-1}\right)=15\)

Answer 1

Đặt \(\frac{8-x}{x-1}\) = y ( y thuộc Z )

Khi đó phương trình trở thành :

xy ( x - y ) = 15

<=> x²y - xy² = 15

Answer 2

ĐKXĐ:...

\(\Leftrightarrow\frac{8x-x^2}{x-1}\left(\frac{x^2-8}{x-1}\right)=15\)

\(\Leftrightarrow\frac{8x-x^2}{x-1}\left(\frac{x^2-8x+8x-8}{x-1}\right)=15\)

\(\Leftrightarrow-\left(\frac{x^2-8x}{x-1}\right)\left(\frac{x^2-8x}{x-1}+8\right)=15\)

Đặt \(\frac{x^2-8x}{x-1}=a\)

\(-a\left(a+8\right)=15\Leftrightarrow a^2+8a+15=0\)

\(\Leftrightarrow\left[{}\begin{matrix}a=-3\\a=-5\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}\frac{x^2-8x}{x-1}=-3\\\frac{x^2-8x}{x-1}=-5\end{matrix}\right.\) \(\Leftrightarrow...\)