Question

Express the rational denominator 1/√3-√2-√1

Answer 1

i know for 1/root3+root2 not -root2 i guess if not pls inform

Sol:
1 / (1 + √2 - √3)

= [1 / (1 + √2) - (√3)] x [(1 + √2) + (√3) / (1 + √2) + (√3)]
= (1 + √2 + √3) / (1 + √2)2 - (√3)2
= (1 + √2 + √3) / (1 + 2 + 2√2) - 3
= (1 + √2 + √3) / 2√2
= [(1 + √2 + √3) / 2√2] x [√2/√2]
= (√2 + 2 + √6) / 4

∴ 1 / (1 + √2 - √3) = (√2 + 2 + √6) / 4.