Question

60/x - 63/x+2 = 1/2

Answer 1

ĐKXĐ: \(x\ne0;x\ne-2\)

\(\frac{60}{x}-\frac{63}{x+2}=\frac{1}{2}\)

\(\Rightarrow120\left(x+2\right)-126x=x\left(x+2\right)\)

\(\Leftrightarrow120x+240-126x=x^2+2x\)

\(\Leftrightarrow240-6x=x^2+2x\)

\(\Leftrightarrow-x^2-8x+240=0\)

\(\Leftrightarrow x^2+8x-240=0\)

\(\Leftrightarrow x^2+20x-12x-240=0\)

\(\Leftrightarrow\left(x^2-12x\right)+\left(20x-240\right)=0\)

\(\Leftrightarrow\left(x-12\right)\left(x+20\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-12=0\\x+20=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=12\left(TM\right)\\x=-20\left(TM\right)\end{matrix}\right.\)

Vậy phương trình có tập nghiệm là: S ={12; -20}