Jawab:
(a.)  5p ÷ 3q       = ¹/₃₃ (70 + 25√3)
(b.)  (p-q) ÷ q      = ¹/₁₁ (3 + 5√3)
(c.)  (p+q) ÷ (p-q) = ⅓ (5√3)
(d.)  (3p+q) ÷ 3q = ¹/₃₃ (53 + 15√3)

Penjelasan:
Diketahui nilai
p = 5+√3     q = 5-√3

(a.)  5p ÷ 3q
= 5(5+√3) ÷ 3(5-√3)
= ⁵/₃ (5+√3) ÷ (5-√3)
= ⁵/₃ (5+√3)² ÷ (5-√3)(5+√3)
= ⁵/₃ (5² + 2(5)√3 + (√3)²) ÷ (5²-(√3)²)
= ⁵/₃ (25 + 10√3 + 3) ÷ (25-3)
= ⁵/₃ (28 + 10√3) ÷ (22)
= ⁵/₃ (2(14) + 2(5)√3) ÷ (2(11))
= ⁵/₃ (14 + 5√3) ÷ 11
= ⁵/₃₃ (14 + 5√3)
= ¹/₃₃ (14(5) + 5(5)√3)
= ¹/₃₃ (70 + 25√3)

(b.)  (p-q) ÷ q
= (5+√3-(5-√3)) ÷ (5-√3)
= (5+√3-5+√3) ÷ (5-√3)
= (2√3) ÷ (5-√3)
= (2√3)(5+√3) ÷ (5-√3)(5+√3)
= (5(2√3)+√3(2√3)) ÷ (5²-(√3)²)
= (10√3 + 6) ÷ (25-3)
= (10√3 + 6) ÷ 22
= (2×5√3 + 2×3) ÷ (2×11)
= ¹/₁₁ (3 + 5√3)

(c.)  (p+q) ÷ (p-q)
= (5+√3+5-√3) ÷ (5+√3-(5-√3))
= (5+√3+5-√3) ÷ (5+√3-5+√3)
= (5+5) ÷ (√3+√3)
= (2(5)) ÷ (2√3)
= 5 ÷ √3
= 5√3 ÷ (√3²)
= 5√3 ÷ 3
= ⅓ (5√3)

(d.)  (3p+q) ÷ 3q
= (3(5+√3)+5-√3) ÷ (3(5-√3))
= (3(5)+3√3+5-√3) ÷ (3(5)-3√3)
= (15+3√3+5-√3) ÷ (15-3√3)
= (20+2√3) ÷ (15-3√3)
= (2(10)+2(√3)) ÷ (3(5)-3(√3))
= (2(10+√3)) ÷ (3(5-√3))
= ⅔ × (10+√3) ÷ (5-√3)
= ⅔ × (10+√3)(5+√3) ÷ [(5-√3)(5+√3)]
= ⅔ × 10(5+√3)+√3(5+√3) ÷ (5²-(√3)²)
= ⅔ × (50 + 10√3 + 5√3 + 3) ÷ (25-3)
= ⅔ × (53 + 15√3) ÷ (22)
= ²/₆₆ × (53 + 15√3)
= ¹/₆₆ × (2(53) + 2(15√3))
= ¹/₆₆ (106 + 30√3)
= (2×53 + 2×15√3) ÷ (2×33)
= (53 + 15√3) ÷ 33
= ¹/₃₃ (53 + 15√3)

(xcvi)