Question

Rezolvaţi în mulţimea numerelor reale,ecuaţia : $\frac{x-1}{3} + \frac{1}{5} =\frac{x-2}{2} +\frac{2}{3}$

Answer 1

$\displaystyle \frac{x-1}{3}+\frac{1}{5}=\frac{x-2}{2}+\dfrac{2}{3}\,\,\Bigg|\cdot 2\cdot 3\cdot 5 \\ \\\Leftrightarrow\, 10(x-1)+6 = 15(x-2)+10\cdot 2\\ \\ \Leftrightarrow\,10x-10+6 = 15x-30+20 \\ \\ \Leftrightarrow\,15x-10x = -4+10\\ \\\Leftrightarrow\, 5x = 6 \\ \\ \Leftrightarrow\,\boxed{x = \dfrac{6}{5}}$