# 1/sqrt.3 + 1/(3 + sqrt.3) + 1/(sqrt.3 – 3) is

The value of

(a) 3

(b) sqrt.3

(c) 0

(d) None of these

**Answer: (c) 0 **

**Solution:-**

1/√3 + 1/(3 + √3) + 1/(√3 – 3)

√3/√3√3 + (3 – √3)/(3 + √3) (3 – √3) + (√3 + 3)/(√3 – 3) (√3 + 3)

√3/3 + (3 – √3)/(9 – 3) + (√3 + 3)/(3 – 9)

√3/3 + (3 – √3)/6 + (√3 + 3)/(-6)

√3/3 + (3 – √3)/6 – (√3 + 3)/(6)

√3/3 + (3 – √3 – √3 – 3)/6

√3/3 – 2√3/6

= √3/3 – √3/3

= 0

Hence, the correct answer is option (c) 0.