Question

√7 - √3 / √7 + √3, racionalizar, con procedimiento por favor

Answer 1

=(√7-√3)/(√7+√3)
=(√7-√3)×(√7-√3)/(√7+√3)×(√7-√3)
=(7+3-2√21)/(7-3)
=(10-2√2)/4
=2(5-√2)/4
=(5-√2)/2

Answer 2

$\frac{ \sqrt{7} - \sqrt{3} }{ \sqrt{7} + \sqrt{3} } = \frac{ \sqrt{7} - \sqrt{3} }{ \sqrt{7} + \sqrt{3} } \times \frac{ \sqrt{7} + \sqrt{3} }{ \sqrt{7 } + \sqrt{3 } } \\ = \frac{7 + 3 - 2 \sqrt{21} }{7 - 3} using \: formulae \: of \: {(x + y)}^{2} \: in \: numerator \: \: \\ and \: {x}^{2} - {y}^{2} \: in \: denominator \\ \\ = \frac{10 - 2 \sqrt{21} }{4} = \frac{5 - \sqrt{21} }{2}$