4 years ago

Hey Im confused can you help me with this?

Mathematics

1 answer:

Tom [10]4 years ago

3 0

From left to right the numbers go. positive,negative, negative, positive. Put them in that order.

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(sqrt(6))/(8+\sqrt(10))

valkas [14]

Answer:

$\frac{4\sqrt{6}-\sqrt{15}}{27}$

Step-by-step explanation:

$\frac{\sqrt{6} }{8+\sqrt{10} } \\\\\mathrm{Multiply\:by\:the\:conjugate}\:\frac{8-\sqrt{10}}{8-\sqrt{10}}\\=\frac{\sqrt{6}\left(8-\sqrt{10}\right)}{\left(8+\sqrt{10}\right)\left(8-\sqrt{10}\right)}\\\\\sqrt{6}\left(8-\sqrt{10}\right)=8\sqrt{6}-2\sqrt{15}\\\left(8+\sqrt{10}\right)\left(8-\sqrt{10}\right)=54\\\\=\frac{8\sqrt{6}-2\sqrt{15}}{54}\\\\\mathrm{Factor}\:8\sqrt{6}-2\sqrt{15}:\quad 2\left(4\sqrt{6}-\sqrt{15}\right)\\\\=\frac{2\left(4\sqrt{6}-\sqrt{15}\right)}{54}\\$

$\mathrm{Cancel\:the\:common\:factor:}\:2\\\\=\frac{4\sqrt{6}-\sqrt{15}}{27}$

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