# How do you simplify this equation 1 into equation 2?

## Equation 1... $\frac{5}{2} {x}^{\frac{3}{2}} - \frac{9}{2} {x}^{\frac{1}{2}} + {x}^{- \frac{1}{2}}$ Equation 2 (simplified version of Equation 1)... (5x^2 - 9x + 2)/(2sqrt(x)

Jul 18, 2018

#### Explanation:

$\frac{5}{2} {x}^{\frac{3}{2}} - \frac{9}{2} {x}^{\frac{1}{2}} + {x}^{- \frac{1}{2}}$,

$= \frac{5 {x}^{\frac{3}{2}}}{2} - \frac{9 {x}^{\frac{1}{2}}}{2} + \frac{1}{x} ^ \left(\frac{1}{2}\right)$,

$= \frac{5 {x}^{\frac{3}{2}} \cdot {x}^{\frac{1}{2}} - 9 {x}^{\frac{1}{2}} \cdot {x}^{\frac{1}{2}} + 1 \cdot 2}{2 {x}^{\frac{1}{2}}}$,

$= \frac{5 {x}^{\frac{3}{2} + \frac{1}{2}} - 9 {x}^{\frac{1}{2} + \frac{1}{2}} + 2}{2 {x}^{\frac{1}{2}}}$,

$= \frac{5 {x}^{2} - 9 x + 2}{2 \sqrt{x}}$, as desired!