To find the value of the given expression, let's simplify it step by step:
(21/4 - 1)(23/4 + 21/2 + 21/4 + 1)
First, let's simplify the expression inside the brackets:
23/4 + 21/2 + 21/4 + 1
To add fractions, we need to have a common denominator. In this case, the common denominator is 4.
23/4 + 21/2 + 21/4 + 1 = 23/4 + (2*21)/4 + 21/4 + 4/4
= (23 + 42 + 21 + 4)/4
= 90/4
= 45/2
Now, let's substitute this value back into the original expression:
(21/4 - 1)(45/2)
= (21/4 - 4/4)(45/2)
= (17/4)(45/2)
To multiply fractions, multiply the numerators together and multiply the denominators together:
= (17 * 45)/(4 * 2)
= 765/8
Therefore, the value of the expression is 765/8.
However, none of the given options match this value. So, the correct answer should be "None".