Question

1/4-3корінь2 - 1/4+3корінь2

Answer 1

$\frac{1}{4 - 3 \sqrt{2} } - \frac{1}{4 + 3 \sqrt{2} } = \frac{4 + 3 \sqrt{2} - (4 - 3 \sqrt{2}) }{(4 - 3 \sqrt{2})(4 + 3 \sqrt{2} )} = \frac{4 + 3 \sqrt{2} - 4 + 3 \sqrt{2} }{(4 - 3 \sqrt{2})(4 + 3 \sqrt{2} )} = \frac{6 \sqrt{2} }{16 - 18} = \frac{6 \sqrt{2} }{ - 2} = - 3 \sqrt{2}$