[tex]x\div5=\dfrac{x}{5},\ x\div3=\dfrac{x}{3}\\\\(x\div5)+(x\div3)=\dfrac{8}{15}\\\\\dfrac{x}{5}+\dfrac{x}{3}=\dfrac{8}{15}\ \ \ \ \ |\cdot15\\\\15\cdot\dfrac{x}{5}+15\cdot\dfrac{x}{3}=15\cdot\dfrac{8}{15}\\\\3\cdot\dfrac{x}{1}+5\cdot\dfrac{x}{1}=1\cdot\dfrac{8}{1}\\\\3x+5x=8\\\\8x=8\ \ \ \ |:8\\\\\boxed{x=1}[/tex]
