Final answer:
The least common denominator (LCD) of the expressions is found by factoring the denominators and combining the unique factors. The LCD is 8x(2x+1), which is not listed exactly in the options provided. The closest option to the correct LCD is a) 2x(20x+16).
Step-by-step explanation:
To Find the LCD of the expressions \(\frac{7}{2x} - \frac{x-2}{20x+16}\), we need to look at their denominators and factor them if possible. The first denominator is 2x, which is already in simplest form. The second denominator, 20x+16, can be factored as 4(5x+4), which simplifies to 4 \times 2(2x+1).
So, to find the least common denominator (LCD), we need to combine the unique factors from both denominators. The first denominator has a factor of 2x, and the second has 4 and (2x+1).
The LCD is the product of these unique factors: 2x \times 4 \times (2x+1). Simplifying this, we obtain 8x(2x+1). Therefore, the LCD is not directly listed in the options provided. However, the option closest to our result, considering that 8x is a multiple of 2x, would be a) 2x(20x+16).