This equation is not correct. The sum of the arcsine function values is not simply equal to the arcsine function of the sum of the arguments. The correct equation for arcsine function addition formula is:

arcsin(a) + arcsin(b) = arcsin(asqrt(1 - b^2) + bsqrt(1 - a^2))

Therefore, the equation "arcsin(3x/5) + arcsin(4x/5) = arcsin(x)" is incorrect.