Solve for x:
y = x/sqrt(x^2+1)
y = x/sqrt(x^2+1) is equivalent to x/sqrt(x^2+1) = y:
x/sqrt(x^2+1) = y
Multiply both sides by sqrt(x^2+1):
x = y sqrt(x^2+1)
x = sqrt(x^2+1) y is equivalent to sqrt(x^2+1) y = x:
y sqrt(x^2+1) = x
Raise both sides to the power of two:
y^2 (x^2+1) = x^2
Expand out terms of the left hand side:
y^2+x^2 y^2 = x^2
Subtract x^2+y^2 from both sides:
x^2 (y^2-1) = -y^2
Divide both sides by y^2-1:
x^2 = -y^2/(y^2-1)
Take the square root of both sides:
Answer: |x = i sqrt(y^2/(y^2 - 1)) or x = -i sqrt(y^2/(y^2 - 1))