Sketching graph-please help me check if this is correct

the problem is y=(1/x)+[1/(x+1)] I have to sketch the graph.

Listed below are my work.

let y=f(x)
f'(x)=[-1/x(^2)]-[1/((x+1)^2)]

I made f'(x)=0 and found that x can't be solved. Does this mean there are no critical points?

Asymptotes at x=0 and x=-1

Attached is the graph I drew.

Is this correct? What happens if I can't solve for x?

Thank you!

Yes, the fact that f'(x) means there are no critical points- no max, min, or saddle point, just as your graph shows.