Question

[Nguyễn Thanh Huyền]

\(\frac{120}{x}=1+\frac{1}{6}+\frac{120-x}{x+6}\)

Giải pt

Answer 1

[Duyên]

\(ĐK:x\ne0;x\ne-6\)

⇔ \(\frac{720\left(x+6\right)}{6x\left(x+6\right)}=\frac{6x\left(x+6\right)}{6x\left(x+6\right)}+\frac{x\left(x+6\right)}{6x\left(x+6\right)}+\frac{6x\left(120-x\right)}{6x\left(x+6\right)}\)

\(\Rightarrow720x+4320=6x^2+36x+x^2+6x+720x-6x^2\)

\(\Leftrightarrow6x^2+36x+x^2+6x+720x-6x^2-720x-4320=0\)

\(\Leftrightarrow x^2+42x-4320=0\)

\(\Leftrightarrow x^2+90x-48x-4320=0\)

\(\Leftrightarrow\left(x+90\right)\left(x-48\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x+90=0\\x-48=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=-90\\x=48\end{matrix}\right.\) ( tm )