help please :)

Question

Perform the indicated operations, rationalizing the denominator (solve all please):

 

A) {(√3)/(√6 - 1)} - {(√3)/(√6 + 1)}

 

B) 3√2x {(1/√x + 2) + (2/(√x+1))}

Answer 1

A) To subtract (or add) fractions, we need common denominators. 

Multiply the first fraction by (√6 + 1)/(√6 + 1) and the second fraction by (√6 - 1)/(√6 - 1).

When we multiply the denominators as described above, we end up with 6 - 1 or 5. Our denominators are now rationalized. Whew!

For the numerators, we get √3(√6 + 1) and √3(√6 - 1) which expand to √18 + √3 and √18 - √3, respectively.

When we subtract, we get √18 + √3 - √18 + √3 = 2√3.

Final answer: (2√3)/5

 

B) I'm a bit confused about which terms are under the square root symbol. Is the first term 3√2(x) or 3√(2x)? Is the first fraction (1/√x) + 2 or 1/(√x + 2) or 1/√(x + 2)? Similar question for the send fraction.