Represent the following mixed infinite decimal periodic fractions as common fractions:
(a1/2+2a+2a1/2+1−a1/2−2a−1)⋅a1/2+1a1/2
(a12+2a+2a12+1−a12−2a−1)⋅a12+1a12
=(√a+2(√a)2+2√a+1)−√a−2(√a)2−1))⋅√a+1√a
=[√a+2(√a+1)2−√a−2(√a+1)(√a−1)]⋅√a+1√a
=[√a+2√a+1−√a−2√a−1]√a+1√a(√a+1)
=((√a+2)(√a−1)−(√a−2)(√a+1)a−1)1√a
=[a−√a+2√a−2−(a+√a−2√a−2)a−1]1√a
=[a+√a−2−a+√a+2a−1]1√a
=2√a(a−1)√a=2a−1