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

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) (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.

RELATED QUESTIONS
simplify 1/squareroot of 3+2 + 1/square root of 3-2 This is from... (answered by Boreal)

Solve: {{{3-5x = sqrt(5)}}} some rationalisation, surds? Not sure how to do this. Any (answered by Theo,Edwin McCravy,ikleyn)

Hi! Can you please help me solve this problem? I need to find the area of a right... (answered by richwmiller)

What is 3 1/4 minus 2 7/8. In subtracting fractions. Thank you... (answered by lwsshak3)

what is: 3 2/3 - 1 1/8 Thank You... (answered by jorel1380)

Subtracting fractions please show work thank you... (answered by sachi)

Help please I am confused and need some clarifying on this problem I seem to be getting... (answered by jim_thompson5910)

1/6 + 3/4 = /12 + /12 = This is 1 problem with 2 missing top numbers above the 12's. (answered by richwmiller)

Is this question correct, thank you (1/3x^2 - 2/3) (1/2x - 1/2)= 1/6 x^3 - 1/6 x^2... (answered by Alan3354)