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Oliga [24]
3 years ago
9

What is simplest form of sqrt 2 + sqrt 5 / sqrt 2 - sqrt -5? √2 + √5 / √2 - √-5

Mathematics
1 answer:
Leni [432]3 years ago
6 0

Answer:

\frac{-7-2\sqrt{10}}{3}

Step-by-step explanation:

we have

\frac{\sqrt{2}+\sqrt{5}}{\sqrt{2}-\sqrt{5}}

Simplify

Multiply the expression by  \frac{\sqrt{2}+\sqrt{5}}{\sqrt{2}+\sqrt{5}}

(\frac{\sqrt{2}+\sqrt{5}}{\sqrt{2}-\sqrt{5}})(\frac{\sqrt{2}+\sqrt{5}}{\sqrt{2}+\sqrt{5}})

Apply difference of squares in the denominator

\frac{(\sqrt{2}+\sqrt{5})^2}{(\sqrt{2})^2-(\sqrt{5})^2}

\frac{2+2\sqrt{10}+5}{2-5}

\frac{7+2\sqrt{10}}{-3}

\frac{-7-2\sqrt{10}}{3}

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