Bentuk sederhana dari persamaan berikut adalah . . .

<p>Jawaban : (4√3 + 3√2)/6.</p><p>&nbsp;</p><p>Ingat:</p><ul><li>Penjumlahan pecahan dilakukan dengan cara menyamakan penyebut.</li><li>Merasionalkan bentuk a/√b = a/√b × (√b/√b)</li><li>√b × √b = b</li></ul><p>&nbsp;</p><p>Pembahasan:</p><p>(2√3)/3 + 1/√2 = [√2(2√3)]/3√2 + [3(1)]/3√2</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = (2√6)/3√2 + 3/3√2&nbsp;</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = &nbsp;(2√6 + 3)/3√2&nbsp;</p><p>Kemudian penyebut dirasionalkan dengan cara mengalikan akar sekawan penyebut:</p><p>(2√6 + 3)/3√2 &nbsp;= (2√6 + 3)/3√2 × (√2/√2)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;= [√2(2√6 + 3)]/[√2(3√2)]</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;= (2√12 + 3√2)/(3×2)</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;= (2√(4×3) + 3√2)/6</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;= &nbsp;(2×2√3 + 3√2)/6</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;= &nbsp;(4√3 + 3√2)/6</p><p>&nbsp;</p><p>Jadi, bentuk sederhananya adalah (4√3 + 3√2)/6.</p>