we have the expression
[tex]\frac{8}{3-\sqrt[]{10}}[/tex]
To simplify the given rational expression, multiply numerator and denominator by the conjugate of the denominator
so
[tex]\frac{8}{3-\sqrt[]{10}}\cdot\frac{3+\sqrt[]{10}}{3+\sqrt[]{10}}[/tex][tex]\frac{8}{3-\sqrt[]{10}}\cdot\frac{3+\sqrt[]{10}}{3+\sqrt[]{10}}=\frac{8\cdot(3+\sqrt[]{10})}{3^2-(\sqrt[]{10})^2}[/tex][tex]\frac{8\cdot(3+\sqrt[]{10})}{3^2-(\sqrt[]{10})^2}=\frac{24+8\sqrt[]{10}}{9-10}[/tex][tex]\frac{24+8\sqrt[]{10}}{-1}=-24-8\sqrt[]{10}[/tex]
therefore
The answer is
[tex]-24-8\sqrt[]{10}[/tex]
