Question: Rationalize the denominators and simplify: $\dfrac{√2 +1}{√2 -1}$


Solution:
Given,

$= \dfrac{√2 +1}{√2 -1}$

$= \dfrac{√2 +1}{√2-1} × \dfrac{√2+1}{√2+1}$

$= \dfrac{(√2+1)²}{(√2)²-(1)²}$

$= \dfrac{(√2)² + 2×√2×1 + 1²}{2-1}$

$= \dfrac{2+2√2 +1}{1}$

$= 3 +2√2$
= Answer