\(\dfrac{57}{x+3}-\dfrac{39}{x}=\dfrac{5}{12}\)
\(\Leftrightarrow57.12x-39.12\left(x+3\right)=5x\left(x+3\right)\)
\(\Leftrightarrow684x-468x-1404=5x^2+15x\)
\(\Leftrightarrow216x-1404-5x^2-15x=0\)
\(\Leftrightarrow201x-1404-5x^2=0\)
\(\Leftrightarrow5x^2-201x+1404=0\)
\(\Leftrightarrow5x^2-45x-156x+1404=0\)
\(\Leftrightarrow5x\left(x-9\right)-156\left(x-9\right)=0\)
\(\Leftrightarrow\left(5x-156\right)\left(x-9\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}5x-156=0\\x-9=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{156}{5}\\x=9\end{matrix}\right.\)
Chưa học delta thì làm theo cách này nhé :>
Ta có: \(\dfrac{57}{x+3}-\dfrac{39}{x}=\dfrac{5}{12}\)
\(\Leftrightarrow\dfrac{18x-117}{x\left(x+3\right)}=\dfrac{5}{12}\)
\(\Leftrightarrow5x^2+15x=216x-1404\)
\(\Leftrightarrow5x^2-201x+1404=0\)
\(\text{Δ}=201^2-4\cdot5\cdot1404=12321\)
Vì Δ>0 nên phương trình có hai nghiệm phân biệt là:
\(\left\{{}\begin{matrix}x_1=\dfrac{201-111}{10}=9\\x_2=\dfrac{201+111}{10}=\dfrac{156}{5}\end{matrix}\right.\)
