Jawaban:
a. 5
Penjelasan dengan langkah-langkah:
Operasi Pecahan
[tex] \frac{a}{b} \pm \frac{c}{d} = \frac{ad \pm bc}{bd} \\ [/tex]
Merasionalkan Bentuk Akar
[tex]\frac{a}{ \sqrt{b} + \sqrt{c} } = \frac{a}{ \sqrt{b} + \sqrt{c} } \times \frac{ \sqrt{b} - \sqrt{c} }{\sqrt{b} - \sqrt{c}} \\ [/tex]
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[tex] \frac{ \frac{1}{2} - \frac{1}{ \sqrt{5} } }{ \frac{1}{2} + \frac{1}{ \sqrt{5} } } = a + b \sqrt{5} \\ \frac{ \frac{ \sqrt{5} - 2 }{2 \sqrt{5} } }{ \frac{ \sqrt{5} + 2}{2 \sqrt{5} } } = a + b \sqrt{5} \\ \frac{ \sqrt{5} - 2}{ \sqrt{5} + 2} = a + b \sqrt{5} \\ \frac{ \sqrt{5} - 2}{ \sqrt{5} + 2} \times \frac{ \sqrt{5} - 2}{ \sqrt{5} - 2} = a + b \sqrt{5} \\ \frac{ ( \sqrt{5} )^{2} - 2 \sqrt{5} - 2 \sqrt{5} + {2}^{2} }{ ( \sqrt{5} )^{2} - {2}^{2} } = a + b \sqrt{5} \\ \frac{5 - 4 \sqrt{5} + 4}{5 - 4} = a + b \sqrt{5} \\ \frac{9 - 4 \sqrt{5} }{1} = a + b \sqrt{5} \\ 9 - 4 \sqrt{5} = a +b \sqrt{5} \\ \\ \text{diperoleh} \\ a = 9 \\ b = - 4 \\ \text{maka} \\ a + b = 9 + ( - 4) \\ a + b= 9 - 4 \\ \boxed{a + b= 5}[/tex]
Semoga membantu.
Note:
(a + b)(a - b) = a² - b²
(√a)² = a
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