Question

Answer 1

\(a,=-2\sqrt{5}+9\sqrt{5}-24\sqrt{5}-\sqrt{5}=-18\sqrt{5}\\ b,=\dfrac{3+2\sqrt{2}-3+2\sqrt{2}}{9-8}=4\sqrt{2}\\ c,=\left|x-3\right|+x+5=3-x+x+5=8\\ d,=\dfrac{4\left(\sqrt{3}-1\right)}{2}-\dfrac{5\left(\sqrt{3}+2\right)}{-1}+\dfrac{6\left(\sqrt{3}+3\right)}{-6}\\ =2\sqrt{3}-2+5\sqrt{3}+10-\sqrt{3}-3=6\sqrt{3}-5\\ e,=\dfrac{a+\sqrt{ab}+b-\sqrt{ab}}{\sqrt{a}+\sqrt{b}}\cdot\dfrac{\sqrt{ab}\left(\sqrt{b}-\sqrt{a}\right)\left(\sqrt{a}+\sqrt{b}\right)}{\sqrt{ab}\left(a+b\right)}\\ =\dfrac{\left(a+b\right)\left(\sqrt{b}-\sqrt{a}\right)}{a+b}=\sqrt{b}-\sqrt{a}\)