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Abstract In this paper, we give a straightforward approach to obtaining the solution of the Diophantine equation 1w+1x+1y+1z=12 $\frac{1}{w} + \frac{1}{x} + \frac{1}{y} + \frac{1}{z} = \frac{1}{2}$. We also establish that the Diophantine equation 1w+1x+1y+1z=mn $\frac{1}{w} + \frac{1}{x} + \frac{1}{y} + \frac{1}{z} = \frac{m}{n}$ for any two positive integers m and n has only a finite number of solutions in the positive integers w,x,y $w, x, y$, and z.