Question

Rationalize the denominator of sqrt5 - sqrt3 / sqrt5 + sqrt3​

Answer 1

Answer:

$4 - \sqrt{15}$

Step-by-step explanation:

$\frac{ \sqrt{5} - \sqrt{3} }{ \sqrt{5} + \sqrt{3} }$

=

$\frac{( \sqrt{5} - \sqrt{3})( \sqrt{5} - \sqrt{3})}{( \sqrt{5} + \sqrt{3})( \sqrt{5} - \sqrt{3})}$

=

$\frac{ ({ \sqrt{5} - \sqrt{3} })^{2} }{ ({ \sqrt{5} })^{2} - ({ \sqrt{3} })^{2} }$

=

$\frac{({ \sqrt{5} })^{2} +({ \sqrt{3} })^{2} - 2 \times \sqrt{5} \times \sqrt{3}}{5 - 3}$

=

$\frac{5 + 3 - 2 \times \sqrt{5 \times 3} }{2}$

=

$\frac{8 - 2 \times \sqrt{15} }{2}$

=

$\frac{2(4 - \sqrt{15}) }{2}$

=

$4 - \sqrt{15}$

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