Final answer:
The least common denominator of 5x², 3x, and 8x-32 is 120x³-480x².
Step-by-step explanation:
To find the least common denominator (LCD) of the given expressions, we need to factor the denominators and then find the product of the common and unique factors. Let's start by factoring the denominators:
- 5x² factors into 5 and x².
- 3x and 8x-32 do not factor further.
Now, the least common denominator can be found by multiplying all the common and unique factors:
Therefore, the LCD of 5x² and 3x (8x-32) is 15x²(8x-32) = 120x³-480x².
Learn more about Finding least common denominator in algebraic expressions