\frac{4 \sqrt{3}}{2-\sqrt{2}}-\frac{30}{4 \sqrt{3}-\sqrt{18}}-\frac{\s

1.	\frac{4 \sqrt{3}}{2-\sqrt{2}}-\frac{30}{4 \sqrt{3}-\sqrt{18}}-\frac{\sqrt{18}}{3-\sqrt{12}}
Answer» [1] = (4√3) / (2-√2) = (4√3)(2+√2) / (2-√2)(2+√2) = (8√3+4√6) /2 = 4√3+2√6 …………………(1) [2]= 30 / (4√3-√18) = 30*(4√3+√18) /(4√3-√18)(4√3+√18) =( 120√3 +30√18) /(48–18) = 30(4√3+√18) /30 = 4√3 + 3√2 ………………(2) [3]= √18 / (3–2√3) = √18(3+2√3) / (3–2√3) (3+2√3) = (3√18+2√54) /9–12 = (9√2 + 6√6) /-3 = -3√2 -2√6 ………………(3) Now by combining all 3 terms: (4√3+2√6) — (4√3+3√2) — ( -3√2 -2√6) = 4√3+2√6–4√3–3√2+3√2+2√6 = 2√6 + 2√6 = 4√6

\frac{4 \sqrt{3}}{2-\sqrt{2}}-\frac{30}{4 \sqrt{3}-\sqrt{18}}-\frac{\sqrt{18}}{3-\sqrt{12}}

Answer»

[1] = (4√3) / (2-√2) = (4√3)(2+√2) / (2-√2)(2+√2)

= (8√3+4√6) /2

= 4√3+2√6 …………………(1)

[2]= 30 / (4√3-√18)

= 30*(4√3+√18) /(4√3-√18)(4√3+√18)

=( 120√3 +30√18) /(48–18)

= 30(4√3+√18) /30

= 4√3 + 3√2 ………………(2)

[3]= √18 / (3–2√3)

= √18(3+2√3) / (3–2√3) (3+2√3)

= (3√18+2√54) /9–12

= (9√2 + 6√6) /-3

= -3√2 -2√6 ………………(3)

Now by combining all 3 terms:

(4√3+2√6) — (4√3+3√2) — ( -3√2 -2√6)

= 4√3+2√6–4√3–3√2+3√2+2√6

= 2√6 + 2√6

= 4√6