In the video, Kanye is greeted by his girlfriend's mother and talk show host, Kris, with a hug and a kiss on the cheek. The pair later sit down to chat about his new family, looking relaxed and happy in each other's company.
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While it has been speculated that Kanye and Kris haven't got on in the past, their affectionate greeting on the show seemed to dispel any such rumours.
The notoriously private rapper has also shown how eager he is to support his girlfriend's family, by releasing the first pictures of North on Kris' talk show and reportedly turning down several media offers. The promise of seeing the baby for the first time will no doubt boost ratings for the programme.
Kim and Kanye have also been living with Kim's mother in her Calabasas mansion while their own home is being refurbished.
Other members of the Kardashian clan are due to appear on Friday's episode. Kris' daughters Kendall and Kylie Jenner will chat to their mother about their fashion line, and are set to "take over the runway" with their stylish pieces. Earlier this month they paid a visit to their PacSun pop-up store in New York City to promote their autumn collection.