Answer:
[tex]\frac{-7-2\sqrt{10}}{3}[/tex]
Step-by-step explanation:
we have
[tex]\frac{\sqrt{2}+\sqrt{5}}{\sqrt{2}-\sqrt{5}}[/tex]
Simplify
Multiply the expression by [tex]\frac{\sqrt{2}+\sqrt{5}}{\sqrt{2}+\sqrt{5}}[/tex]
[tex](\frac{\sqrt{2}+\sqrt{5}}{\sqrt{2}-\sqrt{5}})(\frac{\sqrt{2}+\sqrt{5}}{\sqrt{2}+\sqrt{5}})[/tex]
Apply difference of squares in the denominator
[tex]\frac{(\sqrt{2}+\sqrt{5})^2}{(\sqrt{2})^2-(\sqrt{5})^2}[/tex]
[tex]\frac{2+2\sqrt{10}+5}{2-5}[/tex]
[tex]\frac{7+2\sqrt{10}}{-3}[/tex]
[tex]\frac{-7-2\sqrt{10}}{3}[/tex]
