Final answer:
The least common denominator for the expression is (9h^2 - y^2)(3h + y), as it includes all unique factors from both denominators after factoring the difference of squares.
Step-by-step explanation:
To find the least common denominator for the expression (2h + y) / (9h^2 - y^2) - 4h^2 / (3h + y), we need to factorize where possible and determine the lowest common multiple of the denominators. The first denominator, 9h^2 - y^2, is a difference of squares and can be factored into (3h + y)(3h - y). When you compare the two denominators, you can see that (3h + y) already appears as part of the first denominator after factoring. Therefore, the least common denominator must include both factors (3h + y) and (3h - y) from the first denominator, as well as being able to be divided by the second denominator, (3h + y). The least common denominator that meets these criteria is (9h^2 - y^2)(3h + y), as this includes all unique factors from both denominators.