Question

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

Answer 1

ANSWER

$\frac{5( \sqrt{11} + \sqrt{3} )} {8}$

EXPLANATION

The given rational function is

$\frac{5}{ \sqrt{11} - \sqrt{3}}$

We need to rationalize the denominator by multiplying both the numerator and the denominator by the conjugate of

$\sqrt{11} - \sqrt{3}$

which is

$\sqrt{11} + \sqrt{3}$

When we rationalize we obtain:

$\frac{5( \sqrt{11} + \sqrt{3} )}{(\sqrt{11} - \sqrt{3} )( \sqrt{11} + \sqrt{3} )}$

The denominator is now a difference of two squares:

$(a - b)(a + b) = {a}^{2} - {b}^{2}$

We apply this property to get

$\frac{5( \sqrt{11} + \sqrt{3} )}{( \sqrt{11}) ^{2} - ( \sqrt{3}) ^{2} )}$

$\frac{5( \sqrt{11} + \sqrt{3} )}{11 - 3}$

This simplifies to

$\frac{5( \sqrt{11} + \sqrt{3} )} {8}$

Or

$\frac{5 } {8}\sqrt{11} + \frac{5 } {8}\sqrt{3}$

Answer 2

Answer:

B

Step-by-step explanation: