Toán 2x/(x-2) – 5/(x-3) = 5/(x^2 – 5x + 6) help :< 02/12/2021 By Serenity 2x/(x-2) – 5/(x-3) = 5/(x^2 – 5x + 6) help :<
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=$\frac{1}{2}$ Trả lời
$\dfrac{2x}{x-2}-\dfrac{5}{x-3}=\dfrac{5}{x^2-5x+6}\,\,\,(x\ne2;\,x\ne3)\\⇔\dfrac{2x}{x-2}-\dfrac{5}{x-3}=\dfrac{5}{(x-2)(x-3)}\\⇔\dfrac{2x(x-3)-5(x-2)}{(x-2)(x-3)}=\dfrac{5}{(x-2)(x-3)}\\⇔2x(x-3)-5(x-2)=5\\⇔2x^2-6x-5x+10=5\\⇔2x^2-11x+5=0\\⇔2x^2-x-10x+5=0\\⇔x(2x-1)-5(2x-1)=0\\⇔(2x-1)(x-5)=0\\⇔\left[\begin{array}{}2x-1=0\\x-5=0\end{array}\right.\\⇔\left[\begin{array}{}x=\dfrac{1}{2}\\x=5\end{array}\right.\text{ (thoả mãn)}$ Trả lời
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=$\frac{1}{2}$
$\dfrac{2x}{x-2}-\dfrac{5}{x-3}=\dfrac{5}{x^2-5x+6}\,\,\,(x\ne2;\,x\ne3)\\⇔\dfrac{2x}{x-2}-\dfrac{5}{x-3}=\dfrac{5}{(x-2)(x-3)}\\⇔\dfrac{2x(x-3)-5(x-2)}{(x-2)(x-3)}=\dfrac{5}{(x-2)(x-3)}\\⇔2x(x-3)-5(x-2)=5\\⇔2x^2-6x-5x+10=5\\⇔2x^2-11x+5=0\\⇔2x^2-x-10x+5=0\\⇔x(2x-1)-5(2x-1)=0\\⇔(2x-1)(x-5)=0\\⇔\left[\begin{array}{}2x-1=0\\x-5=0\end{array}\right.\\⇔\left[\begin{array}{}x=\dfrac{1}{2}\\x=5\end{array}\right.\text{ (thoả mãn)}$