SOLUTION: This is surds, rationalisation . 1/√3 +1 - √3 -1/2√3 Answer is 2√3 -3/3 All fractions. Thank you

Algebra ->  Equations -> SOLUTION: This is surds, rationalisation . 1/√3 +1 - √3 -1/2√3 Answer is 2√3 -3/3 All fractions. Thank you       Log On


   

Question 1209535: This is surds, rationalisation .
1/√3 +1 - √3 -1/2√3
Answer is 2√3 -3/3
All fractions.
Thank you
Answer by CPhill(1987) About Me  (Show Source):
You can put this solution on YOUR website!
Here's how to rationalize and simplify the expression:
1/√3 + 1 - (√3 - 1) / (2√3)
1. **Rationalize the first term:**
Multiply the numerator and denominator by the conjugate of the denominator:
(1 / (√3 + 1)) * ((√3 - 1) / (√3 - 1)) = (√3 - 1) / (3 - 1) = (√3 - 1) / 2
2. **Rationalize the second term:**
Multiply the numerator and denominator by √3:
((√3 - 1) / (2√3)) * (√3 / √3) = (3 - √3) / 6
3. **Combine the terms:**
(√3 - 1) / 2 - (3 - √3) / 6
4. **Find a common denominator (6):**
(3(√3 - 1)) / 6 - (3 - √3) / 6 = (3√3 - 3 - 3 + √3) / 6 = (4√3 - 6) / 6
5. **Simplify:**
(4√3 - 6) / 6 = (2√3 - 3) / 3
So, the simplified and rationalized form of the expression is (2√3 - 3) / 3.