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Question: $\boxed{S}$ $\boxed{6}$ $109a-193a$ $+ \frac{1}{3}$ $(83a-1095a$ $-\frac{1}{(a(2n)a+(n+1)(2n+1)...

S\boxed{S}

6\boxed{6}

109a−193a109a-193a

+13+ \frac{1}{3}

(83a−1095a(83a-1095a

−1(a(2n)a+(n+1)(2n+1)a)-\frac{1}{(a(2n)a+(n+1)(2n+1)a)}

Answer

The simplified expression is: S=−12643a−1a(2na+(2n+1)(n+1))S = -\frac{1264}{3}a - \frac{1}{a(2na + (2n+1)(n+1))}

Explanation

Solution

The problem required simplifying a given algebraic expression. This involved:

  1. Combining like terms of 'a'.
  2. Simplifying the denominator of the fractional term by expanding and factoring.
  3. Assuming a missing parenthesis and multiplication between a fraction and a parenthesized expression based on common mathematical notation.