Which are the inseparable pairs in Vedanta?

Luv-Kush, Shubha-Labha, Riddhi-Siddhi are inseparable pairs of Vedanta. They signify that you cannot get one without the help of the other.

In Luv-Kush, Kush is a symbol of purity and Luv symbolize the spiritual love. To achieve love one has to be pure in consciousness. To acquire love and inner happiness in life, one may have to use kush, a herb, in daily life. No traditional Hindu ritual is complete without the use of kush grasses. 

Kush is a benevolent satvik detoxifying grass, a symbol of progress and alertness. The word “kushal buddhi” originates from the word kush. In Bhagavad Gita (shloka 6.10) Krishna said that for meditation one should sit on a seat covered with kush grass. The Garuda Purana also described the importance of kush grass in rituals of Panchak death and in cremation of a person whose body has not been found as in natural calamities, by making an effigy of kush grass and completing the rituals. Kush grass is often held in the hands before taking a sankalp.

Kush grass is called Imperata cylindrica Beauv. It is a clean, pure, brittle grass with acrid, cooling, oleaginous, aphrodisiac and diuretic properties. Kush sharbat is a drink routinely used by traditional healers of Chattisgarh. 

In Riddhi-Siddhi, Riddhi is knowledge and Siddhi is perfection.  An obstacle-free life (represented by Ganesha) can be attained only when one masters or tames both knowledge and perfection. 

Riddhi and Siddhi are the two inseparable wives of Lord Ganesha.  

Some symbolize Siddhi as success and Riddhi as prosperity or Riddhi as material abundance and Siddhi as the intellectual and spiritual prowess or Riddhi as prosperity and Siddhi as progress. All are dependent on each other.

Ganesha is said to have two sons, Shubha-Labha. Again the two terms are inseparable from each other. Both the words are written during Diwali on each account book. Shubha is auspiciousness and Labha, profit.

Ram Lakshman are often spoken of as Ram-Lakhan, which signifies that to be in touch with consciousness (Rama) one has to control the mind with an aim (Mana with a Lakshya). 

Other pairs, which are inseparable, are the duals of Rama and Sita, Radha and Krishna, Shiva and Parvati, Brahma and Saraswati and Vishnu and Lakshmi. 

In Rama-Sita, Rama signifies soul consciousness and Sita, the body. It is true for the Krishna and Radha combination. They also signify the dual character of the nature, feminine and masculine natures.

In Brahma and Saraswati, Brahma represents creativity or innovations and Saraswati the art of acquiring pure knowledge. Again both are dependent on each other.

Lakshmi and Vishnu are again inseparable. Vishnu or Krishna is the doer and performer. They signify action in the present. Lakshmi signifies material and spiritual benefits. One can only get the benefits by action in dharma.

Shiva-Parvati is other inseparable word used in Vedic literature. The other is Shiva and Shakti. They represent the true nature of the consciousness, the male and the female energies; the purusha and the prakriti. In terms of computer language, they represent the operational and the application software. No computer can run without both of them. One is knowledge or the information and the other is energy.

Other uncommon pairs are Bharata and Shatrughana of Ramayana. Bharata represents bhakti, devotion and discipline and Shatrughana, victory over the enemy. To win over the Shatru, one has to become Bharata.

In Mahabharata, there is the pair of Nakul (being neutral) and Sahdeva (helping every one). Again they are inseparable. You cannot help unless you are neutral. 

The pairs of modern post Vedic era are Heer-Ranjha; Laila-Majnu, Sheeri-Farhad, Banti and Babli and Veer-Zara. They all symbolize human love relationship.