Simplify 2yn 1 1yn 1 1yn a 2yn y1 1 b 2yn 1 3yn 1

Simplify: (2y^(n + 1) - 1)(y^(n - 1) + 1)/y^n a) 2y^n + y^1 - 1 b) 2y^(n + 1) - 3y^(n + 1) - 1 c) 2y^n + 2y^1 - 1/y^1 - 1/y^n d) 2y^(n - 1) - 3y^(n - 1) - 1

Solution

(2y⁽ⁿ⁺¹⁾-1)(y^(n-1)+1)/yⁿ = (2y^{(n +1 +n-1)} +2y⁽ⁿ⁺¹⁾- y^(n-1) -1)/yⁿ = (2y²ⁿ/yⁿ) +(2y⁽ⁿ⁺¹⁾/yⁿ) –( y^(n-1)/yⁿ) – (1/yⁿ) =

2(y²ⁿ/yⁿ)+2(y⁽ⁿ⁺¹⁾/yⁿ) –( y^(n-1)/yⁿ) – (1/yⁿ) = 2(y ^(2n-n)) +2(y^(n+1-n)) –( y^(n-1-n)) -(1/yⁿ) =

2yⁿ+2y¹-y^-1-1/yⁿ = 2yⁿ+2y¹- 1/y¹- 1/yⁿ. Option c) is the correct answer.

(a^p*a^q = a^(p+q) and 1/a^p = a^-p)