\(\Leftrightarrow\dfrac{5x\left(x-3\right)}{x\left(x-2\right)\left(x-3\right)}+\dfrac{4x\left(x-2\right)}{x\left(x-2\right)\left(x-3\right)}-\dfrac{\left(x-2\right)\left(x-3\right)}{x\left(x-2\right)\left(x-3\right)}=0\)
\(\Leftrightarrow5x^2-15x+4x^2-8x-x^2+5x-6=0\)
\(\Leftrightarrow8x^2-18x-6=0\)
\(\Leftrightarrow4x^2-9x-3=0\)
\(\text{Δ}=\left(-9\right)^2-4\cdot4\cdot\left(-3\right)=129\)
Vì Δ>0 nên phương trình có hai nghiệm phân biệt là:
\(\left\{{}\begin{matrix}x_1=\dfrac{9-\sqrt{129}}{8}\\x_2=\dfrac{9+\sqrt{129}}{8}\end{matrix}\right.\)
ĐKXĐ:\(\left\{{}\begin{matrix}x\ne0\\x\ne2\\x\ne3\end{matrix}\right.\)
\(\dfrac{5}{x-2}+\dfrac{4}{x-3}-\dfrac{1}{x}=0\\ \Leftrightarrow\dfrac{5x\left(x-3\right)}{x\left(x-2\right)\left(x-3\right)}+\dfrac{4x\left(x-2\right)}{x\left(x-2\right)\left(x-3\right)}-\dfrac{\left(x-2\right)\left(x-3\right)}{x\left(x-2\right)\left(x-3\right)}=0\\ \Leftrightarrow\dfrac{5x^2-15x+4x^2-8x-x^2+5x-6}{x\left(x-2\right)\left(x-3\right)}=0\\ \Rightarrow8x^2-18x-6=0\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{9+\sqrt{129}}{8}\left(tm\right)\\x=\dfrac{9-\sqrt{129}}{8}\left(tm\right)\end{matrix}\right.\)
giải giúp mình câu c với ạ, mình cảm ơnnnnn
