Answer
$\dfrac{6}{2-\sqrt{7}}=-4-2\sqrt{7}$
Work Step by Step
$\dfrac{6}{2-\sqrt{7}}$
Multiply the numerator and the denominator by the conjugate of the denominator and simplify :
$\dfrac{6}{2-\sqrt{7}}=\dfrac{6}{2-\sqrt{7}}\cdot\dfrac{2+\sqrt{7}}{2+\sqrt{7}}=\dfrac{6(2+\sqrt{7})}{2^{2}-(\sqrt{7})^{2}}=...$
$...=\dfrac{6(2+\sqrt{7})}{4-7}=\dfrac{6(2+\sqrt{7})}{-3}=-2(2+\sqrt{7})=-4-2\sqrt{7}$