The product of the rational expressions (X + 6)/(X + 3) and (X - 6)/(X - 3) is (X² - 36)/(X² - 9), by multiplying the numerators and denominators respectively, which both simplify as difference of squares.
To find the product of the rational expressions (X + 6)/(X + 3) and (X - 6)/(X - 3), you simply multiply the numerators together and the denominators together. Here's how you do it:
Multiply the numerators: (X + 6) * (X - 6)
Multiply the denominators: (X + 3) * (X - 3)
Simply expand the expressions and combine like terms if possible.
The simplified form of the product can be found by first noting that (X + 6) * (X - 6) is a difference of two squares, which simplifies to X² - 36. The denominators also represent a difference of squares, simplifying to X² - 9.
Putting it all together, the final expression is (X² - 36)/(X² - 9), which is the product of the two given rational expressions.