How do you simplify this equation 1 into equation 2?

Equation 1...
5/2 x^(3/2) - 9/2 x^(1/2) + x^(- 1/2)52x3292x12+x12

Equation 2 (simplified version of Equation 1)...
(5x^2 - 9x + 2)/(2sqrt(x) 5x29x+22x

1 Answer
Jul 18, 2018

Please see Explanation.

Explanation:

5/2x^(3/2)-9/2x^(1/2)+x^(-1/2)52x3292x12+x12,

=(5x^(3/2))/2-(9x^(1/2))/2+1/x^(1/2)=5x3229x122+1x12,

={5x^(3/2)*x^(1/2)-9x^(1/2)*x^(1/2)+1*2}/(2x^(1/2))=5x32x129x12x12+122x12,

={5x^(3/2+1/2)-9x^(1/2+1/2)+2}/(2x^(1/2))=5x32+129x12+12+22x12,

=(5x^2-9x+2)/(2sqrtx)=5x29x+22x, as desired!