What is the best way of resolving an expression with square roots in denominator?I was resolving the following question from my textbook:Write each of the following expressions as a single fraction, simplifying your answer where possible: 4 − 1 12 + 10 3 I have resolved it this way: 4 12 3 12 3 − 3 12 3 + 10 12 12 3 = 4 36 − 3 + 10 4 3 36 = 24 − 3 + 20 3 6 while in the textbook it is resolved like this: 4 − 1 4 × 3 + 10 3 = 4 − 1 2 3 + 10 3 = 8 3 − 1 + 20 2 3 = 8 3 + 19 2 3 I am wondering did I do it correctly and if so, which way is better?

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What is the best way of resolving an expression with square roots in denominator?I was resolving the following question from my textbook:Write each of the following expressions as a single fraction, simplifying your answer where possible:  4  −      1          12        +      10          3      I have resolved it this way:            4              12                    3                            12                    3              −            3                      12                    3              +            10              12                            12                    3              =            4              36            −              3            +      10              4                    3                    36        =            24      −              3            +      20              3              6  while in the textbook it is resolved like this:  4  −      1          4      ×      3        +      10          3        =  4  −      1          2              3              +      10          3        =            8              3            −      1      +      20              2              3              =            8              3            +      19              2              3            I am wondering did I do it correctly and if so, which way is better?

stacan6t · Accepted Answer

Your answer of            24      −              3            +      20              3              6    =            24      +      19              3              6  matches the answer given by the book within a factor of             3              3      :            24      +      19              3              6    =            8              3            +      19              2              3            Your method was effective in solving the problem, although putting       12        3   as the denominator does not follow the &quot;usual&quot; method of coming up with a &quot;least common multiple&quot; for the final denominator; in this case, we have   (  12  ,  3  )  =  3, and therefore we would use       12    =  2      3   as the final denominator and avoid a couple extra multiplications in the process. But another intent in solving problems like this is often to &quot;rationalize the denominator&quot;, which your method achieves quite effectively. In the end, you&#039;ll want to first make sure that you understand the problem and the solution, and then follow the guidelines of the instructor you are working under: if you have a professor or teacher, match what their expectations are in the final answer form; if it&#039;s just a book or self-learning, try to match &quot;common&quot; notation and approaches that you see.

What is the best way of resolving an expression with square roots in denominator? I was resolving t

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