Question #043fb

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Answer 1 · 2018-02-03T07:49:49

$- 4 + \sqrt{11}$ $-4+sqrt11$

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

$\frac{(3 - 2 \sqrt{11}) (2 - \sqrt{11})}{(2 + \sqrt{11}) (2 - \sqrt{11})}$ $((3-2sqrt11)(2-sqrt11))/((2+sqrt11)(2-sqrt11))$

Let's multiply and expand the terms:

$\frac{6 - 3 \sqrt{11} - 4 \sqrt{11} + 2 {\sqrt{11}}^{2}}{4 - {\sqrt{11}}^{2}}$ $(6-3sqrt11-4sqrt11+2sqrt11^2)/(4-sqrt11^2)$

that's

$\frac{6 - 7 \sqrt{11} + 22}{4 - 11}$ $(6-7sqrt11+22)/(4-11)$

$\frac{28 - 7 \sqrt{11}}{- 7}$ $(28-7sqrt11)/-7$

or, in standard form:

$- 4 + \sqrt{11}$ $-4+sqrt11$