Question

simplify 1/2+√3+2/√5+√3+1/2+√5

Answer 1

there is your answer....

Answer 2

Concept

Rationalisation in elementary algebra is used to eliminate the irrational number present in the denominator.

Find

Simplify 1/(2+√3) + 2/(√5-√3) + 1/(2+√5)

Solution

1/(2+√3) + 2/(√5-√3) + 1/(2+√5)

Let us consider

1/(2+√3)       ............(1)

2/(√5-√3)    ............(2)

1/(2+√5)       ............(3)

(1)+(2)+(3) = solution

Solving Part (1)

1/(2+√3)

Rationalising

1/(2+√3) * (2-√3)/(2-√3)

[1*(2-√3)]/ [(2+√3) * (2-√3)]

(2-√3) / [(2)² - (√3)²]

(2-√3) /(4-3)

= 2-√3

Solving Part 2

2/(√5-√3)

Rationalising

2/(√5-√3) * (√5+√3)/(√5+√3)

[2 *  (√5+√3) ] /  [(√5-√3) *  (√5+√3)]

2 (√5+√3) / [(√5)² - (√3)²]

2 (√5+√3) / (5 - 3)

2 (√5+√3) / 2

=  √5+√3

Solving Part 3

1/(2+√5)

Rationalising

1/(2+√5) * (2-√5)/(2-√5)

[1*(2-√5)] /  [(2+√5)*(2-√5)]

(2-√5) / [(2)² - (√5)²]

(2-√5)/(4-5)

2-√5/(-1)

= √5 -2

Adding (1), (2), (3)

= 2- √3 + √5 +√3 +√5 -2

= 2√5

1/(2+√3) + 2/(√5-√3) + 1/(2+√5) = 2√5

#SPJ2