Weird square root disappearing and flipping fraction upside down?So here I was, making 2 math problems, I was able to solve them, but 2 operations seem a bit intractable to me. Maybe you can help me understand why this is true:The first problem: x = 1 5 − 4 y 4 y = 1 5 − x 4 y = 1 − 5 x 5 y 4 = 5 1 − 5 x Why is it possible to turn y 4 upside down? y = 20 / 1 − 5 xThe second problem: 4 A √ B − √ B = 3 √ B ( 4 A − 1 ) = 3Where does the -√B go? I understand that the -1 comes from the - sign in front of the square root. But where does the other √B go? B = 3 ( 4 A − 1 ) B = ( 3 ( 4 A − 1 ) ) 2 B = 9 ( 4 A − 1 ) 2 Everything, except above the bold text I understand. Maybe I do not understand the full extent of a certain rule which I am familiar with in simpler situations. That's why I think an example would be very useful. I really want to have a deep understand of why these things are true.Greetings, Bowser.

Question

Weird square root disappearing and flipping fraction upside down?So here I was, making 2 math problems, I was able to solve them, but 2 operations seem a bit intractable to me. Maybe you can help me understand why this is true:The first problem:  x  =      1    5    −      4    y        4    y    =      1    5    −  x      4    y    =            1      −      5      x        5        y    4    =      5          1      −      5      x      Why is it possible to turn       y    4   upside down?  y  =  20      /    1  −  5  xThe second problem:  4  A      √    B  −      √    B  =  3      √    B  (  4  A  −  1  )  =  3Where does the -√B go? I understand that the -1 comes from the - sign in front of the square root. But where does the other √B go?      B    =      3          (      4      A      −      1      )        B  =  (      3          (      4      A      −      1      )            )    2    B  =      9          (      4      A      −      1              )        2            Everything, except above the bold text I understand. Maybe I do not understand the full extent of a certain rule which I am familiar with in simpler situations. That&#039;s why I think an example would be very useful. I really want to have a deep understand of why these things are true.Greetings, Bowser.

Ashley Parks · Accepted Answer

First question: if two fractions are equal, then their reciprocals are equal too (the reciprocal of a fraction is the same fraction &quot;turned upside down&quot;, using your terminology).Second question: the B is still there: if you multiply       B    (  4  A  −  1  ) you get indeed   4  A      B    −      B  . It&#039;s called &quot;distributive law&quot;.