How would you find the maximum of this function? $\sin(\frac{1}{x-1})+\sin(\frac{1}{x+1})$ [closed]

Like the title says, I am trying to find the maximum of this function, which seems to be near 0.787. This is to "normalize" the function, so that the maximum is 1, so the x value is what I am looking for. Setting the derivative equal to 0 gives $\frac{\cos(\frac{1}{x+1})}{(x+1)^2}=-\frac{\cos(\frac{1}{x-1})}{(x-1)^2}$. Finding an exact value seems tricky.