Question #043fb

1 Answer
Feb 3, 2018

-4+sqrt114+11

Explanation:

We can multiply both terms of the fraction by the factor 2-sqrt(11)211, and transfer the radical form to the numerator:

((3-2sqrt11)(2-sqrt11))/((2+sqrt11)(2-sqrt11))(3211)(211)(2+11)(211)

Let's multiply and expand the terms:

(6-3sqrt11-4sqrt11+2sqrt11^2)/(4-sqrt11^2)6311411+21124112

that's

(6-7sqrt11+22)/(4-11)6711+22411

(28-7sqrt11)/-7287117

or, in standard form:

-4+sqrt114+11