Simplifying a fraction with radicalsSimplify the following fraction as much as possible ( 8 + 2 15 ) 3 / 2 + ( 8 − 2 15 ) 3 / 2 ( 12 + 2 35 ) 3 / 2 − ( 12 − 2 35 ) 3 / 2 This problem is just driving me insane. I've tried so many different approaches but it keeps becoming a mess for meI worked with conjugates but that won't help. The first step would be to get rid of the exponent.Any help on this problem?

Question

Simplifying a fraction with radicalsSimplify the following fraction as much as possible            (      8      +      2              15                    )                  3                      /                    2                    +      (      8      −      2              15                    )                  3                      /                    2                            (      12      +      2              35                    )                  3                      /                    2                    −      (      12      −      2              35                    )                  3                      /                    2                    This problem is just driving me insane. I&#039;ve tried so many different approaches but it keeps becoming a mess for meI worked with conjugates but that won&#039;t help. The first step would be to get rid of the exponent.Any help on this problem?

Gornil2 · Accepted Answer

Hint:What is&amp;nbsp;(&amp;nbsp;5&amp;nbsp;+&amp;nbsp;3&amp;nbsp;)&amp;nbsp;2&amp;nbsp;and&amp;nbsp;(&amp;nbsp;5&amp;nbsp;−&amp;nbsp;3&amp;nbsp;)&amp;nbsp;2&amp;nbsp;?What is&amp;nbsp;(&amp;nbsp;7&amp;nbsp;+&amp;nbsp;5&amp;nbsp;)&amp;nbsp;2&amp;nbsp;and&amp;nbsp;(&amp;nbsp;7&amp;nbsp;−&amp;nbsp;5&amp;nbsp;)&amp;nbsp;2&amp;nbsp;?Another tip:Please locate and apply the following two formulae.1.&amp;nbsp;(&amp;nbsp;a&amp;nbsp;+&amp;nbsp;b&amp;nbsp;)&amp;nbsp;3&amp;nbsp;+&amp;nbsp;(&amp;nbsp;a&amp;nbsp;−&amp;nbsp;b&amp;nbsp;)&amp;nbsp;3&amp;nbsp;2.&amp;nbsp;(&amp;nbsp;a&amp;nbsp;+&amp;nbsp;b&amp;nbsp;)&amp;nbsp;3&amp;nbsp;−&amp;nbsp;(&amp;nbsp;a&amp;nbsp;−&amp;nbsp;b&amp;nbsp;)&amp;nbsp;3&amp;nbsp;

Lucia Grimes · Accepted Answer

For the nominee, I receive:8&amp;nbsp;+&amp;nbsp;2&amp;nbsp;15&amp;nbsp;3&amp;nbsp;+&amp;nbsp;8&amp;nbsp;−&amp;nbsp;2&amp;nbsp;15&amp;nbsp;3&amp;nbsp;=&amp;nbsp;28&amp;nbsp;5&amp;nbsp;I obtain: for the denominator.12&amp;nbsp;+&amp;nbsp;2&amp;nbsp;35&amp;nbsp;3&amp;nbsp;−&amp;nbsp;12&amp;nbsp;−&amp;nbsp;2&amp;nbsp;35&amp;nbsp;3&amp;nbsp;=&amp;nbsp;52&amp;nbsp;5&amp;nbsp;As a result, I obtain:28&amp;nbsp;5&amp;nbsp;52&amp;nbsp;5&amp;nbsp;=&amp;nbsp;7&amp;nbsp;13&amp;nbsp;

Simplifying a fraction with radicals Simplify the following fraction as much as possible

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