Solve algebraicly for the exact values of x: 5x/2=1/x+x/4

Solve algebraically for the exact values of  x:    

5X/2      =        1/x       +        x/4

  >     x  =  2/3,   or   -2/3  >        x     =      0.666667     or          x     =        −0.666667

Lets Solve Equation:

5x/2      =     1/x           +     x/4

Multiply all terms by   X   and Cancel:

5xx / 2          =       1      +     xx / 4

5/2x^2         =      1/4x^2         +     1         Simplify Both sides of equation:

5/2x^2         -      1/4x^2        =       1/4x^2       +     1       -     1/4x^2      

Subtract    1/4x^2      from both sides:

9/4x^2        =         1

9/4x^2 / 9 / 4         =           1/9 / 4             Divide both sides by    9/4:

x^2        =       4/9

x          =      +-      sqrt 4/9         (Take Square Root):

Answer     x             =       0.666667,        or                x            =          -0.666667

Check Answers:

plug them in to make sure they work:

x      =     0.666667     (works  in original   equation):

x      =         -0.666667      (works in original equation):

Therefore, the answers,    x   =   0.666667   or       x     =     -0.666667   >   x  =  2/3,   or   -2/3

Hope that helps                                    : )

this is not the answer this is just a question. is this middle school math?

step-by-step explanation:

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