1/(√7 - 2)
We need to multiply the numerator and denominator of 1/(√7 - 2) by √7 + 2, to get
1/(√7 - 2) x (√7 + 2)/(√7 + 2)
= (√7 + 2)/(√7 - 2)(√7 + 2)
We need to apply the formula (a - b)(a + b) = a2 - b2 in the denominator to get
1/(√7 - 2) = (√7 + 2)/(√7)2 - (2)2
= (√7 + 2)/(7 -4)
= (√7 + 2)/3
Therefore, we conclude that on rationalizing the denominator of 1/(√7 - 2), we get (√7 + 2)/3.