If \((\sqrt{5} + \sqrt{3})/(\sqrt{5} - \sqrt{3}) = a + b\sqrt{15}\), then find the value of a.
4
4 is correct.
Rationalise the denominator by multiplying numerator and denominator by \(\sqrt{5} + \sqrt{3}\).
\(\dfrac{(\sqrt{5} + \sqrt{3})^2}{(\sqrt{5})^2 - (\sqrt{3})^2} = \dfrac{5 + 3 + 2\sqrt{15}}{5 - 3} = \dfrac{8 + 2\sqrt{15}}{2}\).
This simplifies to \(4 + \sqrt{15}\).
Comparing with \(a + b\sqrt{15}\) gives a = 4 and b = 1.
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