How do you simplify this equation 1 into equation 2?

Question

Equation 1...
#5/2 x^(3/2) - 9/2 x^(1/2) + x^(- 1/2)#

Equation 2 (simplified version of Equation 1)...
#(5x^2 - 9x + 2)/(2sqrt(x) #

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Answer 1 · 2018-07-18T04:03:38

Please see Explanation.

#5/2x^(3/2)-9/2x^(1/2)+x^(-1/2)#,

#=(5x^(3/2))/2-(9x^(1/2))/2+1/x^(1/2)#,

#={5x^(3/2)*x^(1/2)-9x^(1/2)*x^(1/2)+1*2}/(2x^(1/2))#,

#={5x^(3/2+1/2)-9x^(1/2+1/2)+2}/(2x^(1/2))#,

#=(5x^2-9x+2)/(2sqrtx)#, as desired!