In this article, we consider the problem of finding zeros of two-operator monotone inclusions in real Hilbert spaces, and the second operator has been linearly composed. We suggest an extended splitting method: At each iteration, it mainly solves one resolvent for each operator, respectively. For these two resolvents, the involved two scaling factors can be different from one to the other. Our suggested splitting method generates both primal sequence and dual sequence. By using a direct, not convoluted discussion, under the weakest possible conditions we prove the former's weak convergence to an element of the associated solution set. This method contains one parameter ranging from zero and one, and it recovers an equivalent version of some known method when the parameter is equal to zero. Furthermore, we via a numerical example clarify the necessity of introducing such a parameter.