The three paths are not mutually exclusive. They overlap to a significant extent.  One path cannot exist in isolation.  A practitioner of one path has to necessarily have at least some of the qualities, attributes and knowledge of the other paths. 

Bhakthi is an essential ingredient for all paths. It is not possible to acquire Gnanam or practice Karma, without having a solid foundation of Bhakti.  As C.  Rajagolachari had said (in his introduction to Bhaja Govindham), that: "Knowledge without Bhakti is useless tinsel). 

Likewise it is not possible to develop Bhakti without having experienced Karma or acquired some Gnyanam about Easwara's teachings.

The relationship between Bhakti and Karma is explained by the Paramathma in the following;

The following is an extract from Srimad Bhagavatham by Kamala Subramaniam

Uddhava said: “KRISHNA, my mind is again confused. A little while back you had said: “Performing duties need not be avoided. On the other hand,  do you daily duties and other duties.” Now You are asking me to give up everythimng. Please explain to me the two apparently contradictory pathways.”

“I will explain it to you,” said KRISHNA. “I will have to go back to the beginnings of creation to make it simple to you. When Ishvara created Maya the World was manifested.  The five elements called the Mahabhutas, the Indriyas, the Tanmatras, and later, the many Lokas were manifested.  Ishvara pervades the entire Universe but because of Maya, the Avidya which envelopes the Mind of Man, this University of  the Ishwara  is hidden concealed. Man gets involved in the illusion: ‘I am the doer.’ ‘ I am enjoying the fruits of my action,’ and such like. This again leads to further details about actions: ‘You shall do this’ and ‘this act is forbidden.’ It is then said that certain acts should be performed for enhancing the Sattvic nature in Man. When the Sattvic nature gains ascendancy the mind becomes clear. Once the mind is clear, it is up to Man to rid himself of the bondage called “action.”

“The Mind should now be trained to discard its attachment to the World of action. Here Bhakti replaces Karma---action.  Abandon everything else and take refuge in the feet of the Ishvara. To avoid the many pitfalls which beset the journey towards the Brahman, Bhakti has to be practiced constantly. Once the Brahman is realised there is no need for action since it ceases to have any significance. This Jiva, this Ishvara was the Seer and there was nothing to be seen. There then appeared the World made up of the elements. Ishvara Himself assumes the form of the Gunas and the play of the Gunas too.  Even as a cloth is made up of the Warp and woof this entire Universe is but a display of Ishvara.

“When two pieces of bamboo rub against each other fire is produced and this fire, after destroying  the entire forest of bamboos, becomes assuaged and is not to be seen. Even so, this body made up of the combination of the elements and the Gunas gets destroyed when its Avidya is gone. And when Avidya, the veil of ignorance is withdrawn, the jivatma becomes one with the Paramathma and there is no longer a separate entity for it since the Ego, the feeling of “I” has been destroyed.

“The Tree by name Samsara has two seeds; Papa and Punya. Hundreds of Vasanas are the roots of this tree. The trunk is made up of the three Gunas. The five elements form the branches and the life-giving sap is made up of the Tanmatras like Shabda, Sparsha, Rupa, Rasa and Gandha. The eleven Indriyas are the further branches of the large branches.

“The Jivatma and the Paramatma are the two eagles which have built their nests in this tree. Happiness and sorrow are the two fruits of this tree. Grihastas who are involved in the pleasures of this World of illusion taste one of the fruits and that fruit is sorrow. Sanyasis, the wise ones, who have abandoned worldly things knowing them to be unreal, taste of the other fruit, eternal happiness.

“So, Uddhava, cut down this tree of Samsara with the power of your intellect. Destroy it and you will be free to reach Me. When you have tasted this fruit once nothing else will seem attractive to you. You can walk in the World of Men with a free mind since you will not be involved in the actions you have to perform as long as you are alive. Your thoughts will be on me and your freedom is assured.”