# Simplify (5 + Sqrt3)/(5 - Sqrt3) + (5 - Sqrt3)/(5 + Sqrt3) - Mathematics

Simplify:

(5 + sqrt3)/(5 - sqrt3) + (5 - sqrt3)/(5 + sqrt3)

#### Solution

We know that rationalization factor for sqrt5 - sqrt3 and sqrt5 + sqrt3 are sqrt5 + sqrt3 and sqrt5 - sqrt3  respectively.

We will multiply numerator and denominator of the given expression  (sqrt5 + sqrt3)/(sqrt5 - sqrt3) and (sqrt5 - sqrt3)/(sqrt5 + sqrt3) by sqrt5 + sqrt3 and sqrt5 + sqrt3 respectively, to get

(sqrt5 + sqrt3)/(sqrt5 - sqrt3) xx (sqrt5 + sqrt3)/(sqrt5 + sqrt3) + (sqrt5 - sqrt3)/(sqrt5 + sqrt3) xx (sqrt5 - sqrt3)/(sqrt5 - sqrt3) = ((sqrt5)^2 + (sqrt3)^2 +  2 xx sqrt5 xx sqrt3)/((sqrt5)^2- (sqrt3)^2)

(5 + 3 + 2sqrt15)/(5- 3) + (5 + 3 - 2sqrt15)/(5 - 3)

= (5 + 3 + 2sqrt15 + 5 + 3 - 2sqrt15)/2

= 16/2

= 8

Hence the given expression is simplified to 8

Concept: Operations on Real Numbers
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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 3 Rationalisation
Exercise 3.2 | Q 5.1 | Page 14

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