The authors consider the equation
where is an unknown function, is a polynomial in the variable and its derivatives and look for exact solutions of the form
, , where the function is the general solution of the linear ordinary differential equation
. They propose the algorithm for searching the parameters , . This approach for the exact solution of the equation (1) the authors call the extended simplest equation method. They apply this method to the Sharma-Tasso-Olver and the Burgers-Huxley equations. New exact solutions of these equations are obtained.