To simplify this expression, we will first use the trigonometric identity:

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

So, we have:

arcsin(3x/5) + arcsin(4x/5) = arcsin((3x/5)sqrt(1-(4x/5)^2) + (4x/5)sqrt(1-(3x/5)^2))

= arcsin((3x/5)sqrt(1-16x^2/25) + (4x/5)sqrt(1-9x^2/25))

= arcsin((3x/5)sqrt(25/25-16x^2/25) + (4x/5)sqrt(25/25-9x^2/25))

= arcsin((3x/5)sqrt(9/25) + (4x/5)sqrt(16/25))

= arcsin((3x/5)(3/5) + (4x/5)(4/5))

= arcsin(9x/25 + 16x/25)

= arcsin(25x/25)

= arcsin(x)

Therefore, arccsin(3x/5) + arccsin(4x/5) = arccsin(x).