How to handle 1/x + 1/(2x+1), x>0

How to handle 1/x + 1/(2x+1), x>0
in the solver it is not dcp

You will benefit from reading or re-reading the CVX Users’ Guide. Have you read http://cvxr.com/cvx/doc/funcref.html#new-functions ?

help inv_pos

inv_pos Reciprocal of a positive quantity.
inv_pos(X) returns 1./X if X is positive, and +Inf otherwise.
X must be real.

 For matrices and N-D arrays, the function is applied to each element.

  Disciplined convex programming information:
      inv_pos is convex and nonincreasing; therefore, when used in CVX
      specifications, its argument must be concave (or affine).