Simplifying nested/complex fractions with variablesI have the equation x = y + y y 70 + y 90 and I need to solve for x. My calculator has already shown me that it's not necessary to know y to solve this equation, but I can't seem to figure it out. This is how I try to solve it: x = y + y y 70 + y 90 = 2 y ( 70 y + 90 y ) = 2 y ( 90 + 70 y ) = 2 y ⋅ 160 y = 320 y y = 320But according to my calculator, this is not correct. The answer should be 78.75, but I don't know why. Any help would be much appreciated.

Question

Simplifying nested/complex fractions with variablesI have the equation  x  =            y      +      y                      y        70            +              y        90            and I need to solve for x. My calculator has already shown me that it&#039;s not necessary to know y to solve this equation, but I can&#039;t seem to figure it out. This is how I try to solve it:  x  =            y      +      y                      y        70            +              y        90              =  2  y      (          70      y        +          90      y        )    =  2  y      (                  90        +        70            y        )    =  2  y  ⋅      160    y    =            320      y        y    =  320But according to my calculator, this is not correct. The answer should be 78.75, but I don&#039;t know why. Any help would be much appreciated.

hopeloothab9m · Accepted Answer

When manipulating expressions, the most important thing is to think small. Find the smallest part of the expression you can do something with. In this case,            2      y                      y        70            +              y        90            has as the smallest available task add the fractions on the bottom, which gives (only showing that part)      y    70    +      y    90    =            90      y      +      70      y              70      ⋅      90        =            160      y        6300    =            8      y        315  Putting that back in, we now have            2      y              (                        8          y                315            )        =  2  y      (          315              8        y              )    =            630      y              8      y        =      315    4    for   y  ≠  0

Tristian Velazquez · Accepted Answer

Dividing numerator and denominator by y (assuming of course that   y  ≠  0 ),and multiplying them by 70 and 90,  x  =            2              1                  /                70        +        1                  /                90              =                    2        ×        70        ×        90                    90        +        70              =            12600      160        =            315      4

Simplifying nested/complex fractions with variables I have the equation x = y

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