tolong pakai latex, mksh

Bab Bilangan Irrasional
Matematika SMP Kelas IX

dikerjakan terpisah-pisah

(3√2)/(√3 + √6)
= (3√2) (√3 - √6)/(3 - 6)
= -√2 (√3 - √6)
= √12 - √6

(4√3)/(√6 + √2)
= (4√3) (√6 - √2)/(6 - 2)
= √18 - √6

(√6)/(√3 + √2)
= (√6) (√3 - √2)/(3 - 2)
= √18 - √12

lalu disatukan berdasarkan operasi bilangannya

(√12 - √6) - (√18 - √6) + (√18 - √12)
= √12 - √6 - √18 + √6 + √18 - √12
= 0

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≡ Penyelesaian:
[tex]\Rightarrow \frac{3\sqrt{2}}{\sqrt{3}+\sqrt{6}}-\frac{4\sqrt{3}}{\sqrt{6}+\sqrt{2}}+\frac{\sqrt{6}}{\sqrt{3}+\sqrt{2}}[/tex]
[tex]\Rightarrow [(\frac{3\sqrt{2}}{\sqrt{3}+\sqrt{6}}).(\frac{\sqrt{3}-\sqrt{6}}{\sqrt{3}-\sqrt{6}})]-[(\frac{4\sqrt{3}}{\sqrt{6}+\sqrt{2}}).(\frac{\sqrt{6}-\sqrt{2}}{\sqrt{6}-\sqrt{2}})]+[(\frac{\sqrt{6}}{\sqrt{3}+\sqrt{2}}).(\frac{\sqrt3-\sqrt{2}}{\sqrt{3}-\sqrt{2}})][/tex]
[tex]\Rightarrow [\frac{3\sqrt{2}(\sqrt{3}-\sqrt{6})}{-3}]-[\frac{4\sqrt{3}(\sqrt{6}-\sqrt{2})}{4}]+[\frac{\sqrt{6}(\sqrt{3}-\sqrt{2})}{1}][/tex]
[tex]\Rightarrow [-\sqrt{2}(\sqrt{3}-\sqrt{6})]-[\sqrt{3}(\sqrt{6}-\sqrt{2})]+[\sqrt{6}(\sqrt{3}-\sqrt{2})][/tex]
[tex]\Rightarrow [-\sqrt{6}+\sqrt{12}]-[\sqrt{18}-\sqrt{6}}]+[\sqrt{18}-\sqrt{12}][/tex]
[tex]\Rightarrow -\sqrt{6}+\sqrt{12}-\sqrt{18}+\sqrt{6}+\sqrt{18}-\sqrt{12} \\ \leadsto \boxed{0}[/tex]