![\displaystyle \frac{x+1}{2} + \frac{x}{3} = 3\\\\LCM = 6\\\\So, Multiply \ both \ sides \ by \ 6\\\\ (\frac{x+1}{2} * 6) + (\frac{x}{3} * 6) = 3*6\\\\3(x+1) + (x*2) = 18\\\\ 3x + 3 + 2x = 18\\\\5x + 3 = 18\\\\Subtract \ 3 \ to \ both \ sides\\\\ 5x = 18-3\\\\5x = 15\\\\Divide \ both \ sides \ by \ 5\\\\\boxed{ x = 3}\\\\\rule[225]{225}{2}](/tpl/images/2234/5281/0f65c.png)
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