2x/(x-2) – 5/(x-3) = 5/(x^2 – 5x + 6) help :<

2x/(x-2) – 5/(x-3) = 5/(x^2 – 5x + 6) help :<

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  1. Ta có $\frac{2x}{x-2}$ – $\frac{5}{x-3}$ = $\frac{5}{x²-5x+6}$

    ⇔ $\frac{2x(x-3)}{(x-2)(x-3)}$-$\frac{5(x-2)}{(x-3)(x-2)}$=$\frac{5}{(x-3)(x-2)}$

    ⇔2x²-6x-5x+10=5

    ⇔2x²-11x+5=0

    ⇔(x-5)(2x-1)=0

    ⇔x=5 hoặc x=$\frac{1}{2}$

     

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  2. $\dfrac{2x}{x-2}-\dfrac{5}{x-3}=\dfrac{5}{x^2-5x+6}\,\,\,(x\ne2;\,x\ne3)\\⇔\dfrac{2x}{x-2}-\dfrac{5}{x-3}=\dfrac{5}{(x-2)(x-3)}\\⇔\dfrac{2x(x-3)-5(x-2)}{(x-2)(x-3)}=\dfrac{5}{(x-2)(x-3)}\\⇔2x(x-3)-5(x-2)=5\\⇔2x^2-6x-5x+10=5\\⇔2x^2-11x+5=0\\⇔2x^2-x-10x+5=0\\⇔x(2x-1)-5(2x-1)=0\\⇔(2x-1)(x-5)=0\\⇔\left[\begin{array}{}2x-1=0\\x-5=0\end{array}\right.\\⇔\left[\begin{array}{}x=\dfrac{1}{2}\\x=5\end{array}\right.\text{ (thoả mãn)}$

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