Question

What is the following quotient? 5/ sqrt 11 - sqrt 3

Answer 1

`\displaystyle\\(5)/(√(11)-√(3))=?\\\\\\\text{We rationalize the denominator.}\\\\(5)/(√(11)-√(3))=(5(√(11)+√(3)))/((√(11)-√(3))(√(11)+√(3)))=(5(√(11)+√(3)))/((11-3))=\boxed{\bf(5√(11)+5√(3)))/(8)}`

Answer 2

The correct option is b)
`(5√(11)+5√(3))/(8)`

Explanation:

We need to find the quotient of
`(5)/(√(11)-√(3))`,

Rationalizing the above,

By multiply and divide by conjugate of its denominator,

`(5)/(√(11)-√(3)) * (√(11)+√(3))/(√(11)+√(3))`

`(5(√(11)+√(3)))/((√(11)-√(3))(√(11)+√(3)))`

Since,
`(a+b)(a-b)=a^(2)-b^(2)`

`(5√(11)+5√(3))/((11-3))`

simplify,

`(5√(11)+5√(3))/(8)`

Therefore, the correct option is b)
`(5√(11)+5√(3))/(8)`