Question

(2/(√8-√9))-((2*√8)/(8-9))

Answer 1

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$\displaystyle\bf \left(\frac{2}{\sqrt{8}-\sqrt{9}}\right)-\left(\frac{2\sqrt{8}}{8-9}\right)=\frac{2}{\sqrt{8}-\sqrt{9}}-\frac{2\sqrt{8}}{8-9}=$

$\boxed{\bf \frac{2}{\sqrt{8}-\sqrt{9}}=\frac{2\left(\sqrt{8}+\sqrt{9}\right)}{\left(\sqrt{8}-\sqrt{9}\right)\left(\sqrt{8}+\sqrt{9}\right)}=\frac{(2\cdot \sqrt8)+(2\cdot \sqrt9)}{\left(\sqrt{8}\right)^2-\left(\sqrt{9}\right)^2}=\frac{2\sqrt 8 +2\sqrt9}{8-9}= -4\sqrt 2 +6}}$

$\boxed{\bf \frac{2\sqrt{8}}{8-9}=\frac{4\sqrt{2}}{8-9}=\frac{4\sqrt{2}}{-1}=-4\sqrt2}$

$\bf =-4\sqrt{2}-6-\left(-4\sqrt{2}\right)=-4\sqrt{2}-6+4\sqrt{2}}=-6$