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

Question

asked Feb 21, 2019 228k views

2 Answers

Brevleq · Answer 1 · 2019-02-27T18:27:00+0000

ANSWER

$\frac{5( √(11) + √(3) )} {8}$

EXPLANATION

The given rational function is

(5)/( √(11) - √(3))

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

√(11) - √(3)

which is

√(11) + √(3)

When we rationalize we obtain:

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

The denominator is now a difference of two squares:

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

We apply this property to get

(5( √(11) + √(3) ))/(( √(11)) ^(2) - ( √(3)) ^(2) ))

(5( √(11) + √(3) ))/(11 - 3)

This simplifies to

$\frac{5( √(11) + √(3) )} {8}$

Or

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