Question 1121485
<br>
There are an infinite number of solutions; so I can't "show as many different solutions as I can".<br>
A strategy for finding pairs of mixed numbers whose sum is 6 might be<br>
3+n and 3-n<br>
where n is any real number that is not an integer.<br>
A few examples....<br>
n=1/2  -->  3 1/2 and 2 1/2
n=3/7  -->  3 3/7 and 2 4/7
n=1 2/11  -->  4 2/11 and 1 9/11
n=5 2/5  -->  8 2/5 and -2 2/5