Question

What is the least common denominator of the expression below?

(x²) / (9 + x) ÷ (x - 16) / (8x + 2x²)
Options:
a. (x + 4)
b. (x + 4)(x - 4)
c. 2(x + 4)(x - 4)
d. 2x(x + 4)(x - 4)

Answer 1

The least common denominator of the expression is 2x(x + 4)(x - 4). The correct option is d.

Step-by-step explanation:

The least common denominator (LCD) of the expression is d. 2x(x + 4)(x - 4).

To find the LCD, we need to find the common multiples of the denominators. The denominators in this expression are (9 + x), (x - 16), (8x + 2x²).
Factorizing the denominators:
(9 + x) can be factored as 1(x + 9)
(x - 16) is already factored
(8x + 2x²) can be factored as 2x(4 + x)
The common factors are (x + 9), (x - 16), and (4 + x).
Multiplying these factors together, we get 2x(x + 9)(x - 16)(4 + x).