Simplify the following:
(1-sqrt(3))/(1+sqrt(3))
Multiply numerator and denominator of (1-sqrt(3))/(1+sqrt(3)) by sqrt(3)-1:
((1-sqrt(3)) (sqrt(3)-1))/((1+sqrt(3)) (sqrt(3)-1))
(1+sqrt(3)) (sqrt(3)-1) = -1+1 sqrt(3)-sqrt(3)+sqrt(3) sqrt(3) = -1+sqrt(3)-sqrt(3)+3 = 2:
((1-sqrt(3)) (sqrt(3)-1))/(2)
(1-sqrt(3)) (sqrt(3)-1) = -1+1 sqrt(3)-(-sqrt(3))-sqrt(3) sqrt(3) = -1+sqrt(3)+sqrt(3)-3 = 2 sqrt(3)-4:
(2 sqrt(3)-4)/(2)
Factor 2 out of 2 sqrt(3)-4 giving 2 (sqrt(3)-2):
(2 (sqrt(3)-2))/(2)
(2 (sqrt(3)-2))/(2) = 2/2×(sqrt(3)-2) = sqrt(3)-2:
Answer: |sqrt(3)-2
(1-sqrt3)/(1+sqrt3) → (1-sqrt3)(1-sqrt3)/( (1+sqrt3)(1-sqrt3) ) → (1-2sqrt3+3)/(1-3)
→ (4 - 2sqrt3)/(-2) → -2 + sqrt3
.
Simplify the following:
(1-sqrt(3))/(1+sqrt(3))
Multiply numerator and denominator of (1-sqrt(3))/(1+sqrt(3)) by sqrt(3)-1:
((1-sqrt(3)) (sqrt(3)-1))/((1+sqrt(3)) (sqrt(3)-1))
(1+sqrt(3)) (sqrt(3)-1) = -1+1 sqrt(3)-sqrt(3)+sqrt(3) sqrt(3) = -1+sqrt(3)-sqrt(3)+3 = 2:
((1-sqrt(3)) (sqrt(3)-1))/(2)
(1-sqrt(3)) (sqrt(3)-1) = -1+1 sqrt(3)-(-sqrt(3))-sqrt(3) sqrt(3) = -1+sqrt(3)+sqrt(3)-3 = 2 sqrt(3)-4:
(2 sqrt(3)-4)/(2)
Factor 2 out of 2 sqrt(3)-4 giving 2 (sqrt(3)-2):
(2 (sqrt(3)-2))/(2)
(2 (sqrt(3)-2))/(2) = 2/2×(sqrt(3)-2) = sqrt(3)-2:
Answer: |sqrt(3)-2
