Question

simplify by rationalizing the denominator: 4 + root 5 / 4- root 5 + 4- root 5 / 4+ root 5

Answer 1

(4 +√5)/(4 -√5)  + (4 -√5)/(4 +√5)
now dividing and multiplying the first term by (4 +√5) and second term by (4 -√5), we get,
(4 +√5)×(4 +√5)/(4 -√5)×(4 +√5) + (4 -√5)×(4 -√5)/(4 +√5)×(4 -√5)
⇒(4 +√5)²/(16 -5) +  (4 -√5)²/(16 -5)   ( applying (a² -b²) = (a+b)(a -b))
⇒(16 +5 +8√5 +16 +5 - 8√5)/11
⇒42/11

Answer 2

Answer:

(4 +√5)/(4 -√5)  + (4 -√5)/(4 +√5)

now dividing and multiplying the first term by (4 +√5) and second term by (4 -√5), we get,

(4 +√5)×(4 +√5)/(4 -√5)×(4 +√5) + (4 -√5)×(4 -√5)/(4 +√5)×(4 -√5)

⇒(4 +√5)²/(16 -5) +  (4 -√5)²/(16 -5)   ( applying (a² -b²) = (a+b)(a -b))

⇒(16 +5 +8√5 +16 +5 - 8√5)/11

⇒42/11

Step-by-step explanation: