\(\frac{20-x}{3}+\frac{22-x}{4}=\frac{24-x}{5}+\frac{26-x}{6}\)
\(\Leftrightarrow\left(\frac{20-x}{3}-1\right)+\left(\frac{22-x}{4}-1\right)=\left(\frac{24-x}{5}-1\right)+\left(\frac{26-x}{6}-1\right)\)
\(\Leftrightarrow\left(\frac{20-x-3}{3}\right)+\left(\frac{22-x-4}{4}\right)=\left(\frac{24-x-5}{5}\right)+\left(\frac{26-x-6}{6}\right)\)
\(\Leftrightarrow\frac{17-x}{3}+\frac{18-x}{4}=\frac{19-x}{5}+\frac{20-x}{6}\)
\(\Leftrightarrow\left(\frac{17-x}{3}-1\right)+\left(\frac{18-x}{4}-1\right)=\left(\frac{19-x}{5}-1\right)+\left(\frac{20-x}{6}-1\right)\)
\(\Leftrightarrow\left(\frac{17-x-3}{3}\right)+\left(\frac{18-x-4}{4}\right)=\left(\frac{19-x-5}{5}\right)+\left(\frac{20-x-6}{6}\right)\)
\(\Leftrightarrow\frac{14-x}{3}+\frac{14-x}{4}=\frac{14-x}{5}+\frac{14-x}{6}\)
\(\Leftrightarrow\frac{14-x}{3}+\frac{14-x}{4}-\frac{14-x}{5}-\frac{14-x}{6}=0\)
\(\Leftrightarrow\left(14-x\right).\left(\frac{1}{3}+\frac{1}{4}-\frac{1}{5}-\frac{1}{6}\right)=0\)
Vì \(\frac{1}{3}+\frac{1}{4}-\frac{1}{5}-\frac{1}{6}\ne0.\)
\(\Leftrightarrow14-x=0\)
\(\Leftrightarrow x=14-0\)
\(\Leftrightarrow x=14.\)
Vậy phương trình có tập hợp nghiệm là: \(S=\left\{14\right\}.\)
Chúc bạn học tốt!
Phương pháp: Quy đồng
\( \dfrac{{20 - x}}{3} + \dfrac{{22 - x}}{4} = \dfrac{{24 - x}}{5} + \dfrac{{26 - x}}{6}\\ \Leftrightarrow 20\left( {20 - x} \right) + 15\left( {22 - x} \right) = 12\left( {24 - x} \right) + 10\left( {26 - x} \right)\\ \Leftrightarrow 400 - 20x + 330 - 15x = 288 - 12x + 260 - 10x\\ \Leftrightarrow 730 - 35x = 548 - 22x\\ \Leftrightarrow - 13x = - 182\\ \Leftrightarrow x = 14 \)
