Use this rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{2\sqrt{x}+x{x}^{\frac{3}{2}}-1-1\times \sqrt{x}-1}{matrix\times 1-\sqrt{x}+22+\sqrt{x}+1}\]
Simplify \(x{x}^{\frac{3}{2}}\) to \({x}^{\frac{5}{2}}\).
\[\frac{2\sqrt{x}+{x}^{\frac{5}{2}}-1-1\times \sqrt{x}-1}{matrix\times 1-\sqrt{x}+22+\sqrt{x}+1}\]
Simplify \(1\times \sqrt{x}\) to \({x}^{\frac{1}{2}}\).
\[\frac{2\sqrt{x}+{x}^{\frac{5}{2}}-1-{x}^{\frac{1}{2}}-1}{matrix\times 1-\sqrt{x}+22+\sqrt{x}+1}\]
Collect like terms.
\[\frac{2\sqrt{x}+{x}^{\frac{5}{2}}+(-1-1)-\sqrt{x}}{matrix\times 1-\sqrt{x}+22+\sqrt{x}+1}\]
Simplify \(2\sqrt{x}+{x}^{\frac{5}{2}}+(-1-1)-\sqrt{x}\) to \(2\sqrt{x}+{x}^{\frac{5}{2}}-2-\sqrt{x}\).
\[\frac{2\sqrt{x}+{x}^{\frac{5}{2}}-2-\sqrt{x}}{matrix\times 1-\sqrt{x}+22+\sqrt{x}+1}\]
Collect like terms.
\[\frac{(2\sqrt{x}-\sqrt{x})+{x}^{\frac{5}{2}}-2}{matrix\times 1-\sqrt{x}+22+\sqrt{x}+1}\]
Simplify \((2\sqrt{x}-\sqrt{x})+{x}^{\frac{5}{2}}-2\) to \(\sqrt{x}+{x}^{\frac{5}{2}}-2\).
\[\frac{\sqrt{x}+{x}^{\frac{5}{2}}-2}{matrix\times 1-\sqrt{x}+22+\sqrt{x}+1}\]
Simplify \(matrix\times 1\) to \(matrix\).
\[\frac{\sqrt{x}+{x}^{\frac{5}{2}}-2}{matrix-\sqrt{x}+22+\sqrt{x}+1}\]
Collect like terms.
\[\frac{\sqrt{x}+{x}^{\frac{5}{2}}-2}{matrix+(-\sqrt{x}+\sqrt{x})+(22+1)}\]
Simplify \(matrix+(-\sqrt{x}+\sqrt{x})+(22+1)\) to \(matrix+23\).
\[\frac{\sqrt{x}+{x}^{\frac{5}{2}}-2}{matrix+23}\]
(sqrt(x)+x^(5/2)-2)/(matrix+23)
