Sometimes I think of a visibly struggling student as the proverbial canary in the mine, pointing out when something clearly isn't working in the way that I'm teaching something. So my first question is:
Are you sure everyone else is with you? How do you know that 14 students get it and 1 doesn't? I'm thinking back to my own teaching, and that 1 student visibly confused probably means that 4-5 other students are confused too and just hiding it. You don't necessarily have to slow down the entire lesson just for one student, but it could be helpful to check in with other students for understanding in those moments where you see the one student struggling.
The second thing I want to offer a bit of a different take on pairing students up than what you mention. You mention pairing up the struggling student with another struggling student. One method of pairing that's worked well in the research literature is called peer assisted learning strategies (PALS), where you are pairing up a struggling student with a student who's not necessarily at the top of the class, but maybe just a little bit about average in the class. You can start by having the student who understands the concept tutoring the struggling student. Then they can switch roles and you can have the struggling student tutor the student who understands it better, so that both have the opportunity to practice being the teacher and the student.
If you wanted to do this as an entire class, you could divide the class in half, and pair the student at the bottom of the lower half with the student at the bottom of the upper half, and so on and so forth, so that the most struggling student is paired with the average student, and the student just at the average is paired with the top student. You could assign the partners, and assign everyone to be A and B, and then that way a student wouldn't necessarily know they've been assigned as the "less smart" one in the pair.
The final thing I want you to think about is looking at having students occasionally work in groups on more complex problems that have multiple ways of reaching a solution and invite mathematical dialogue and collaboration. These are known in the literature as groupworthy tasks, as in a task that's worthy to be worked on by a group of students. Here's some examples of what these tasks look like at the elementary school level: http://cimath.org/tasks-for-download/ . Here's another site that offers some more advanced tasks that might be a good starting point for a high school class: http://nrich.maths.org/public/leg.php