Answer:
(6m² + 12m + 2) / (6m + 1)
Explanation:
multiply both sides by m.
we get m² - 1 = 6m
move the -1 to the other side, so it becomes +1
m² = 6m + 1
so m² + 1/m² = (6m + 1) + 1/(6m + 1)
get a common denominator by squaring (6m + 1)
(6m + 1)².
we now have (6m + 1)² / (6m + 1) + 1/(6m + 1).
we now add the numerators.
(6m + 1)² + 1 = (6m² + 6m + 6m + 1) + 1 = 6m² + 12m + 2.
numerator over denominator = (6m² + 12m + 2) / (6m + 1)