7. \( f(x)=\frac{x^{3}}{2}-3 x^{-2}-2 x^{3}-x^{3 / 2} \)

Calculate or simplify the expression \( (x^3)/(2)-3*(1/x^2)-2*x^3-x^(3/2) \). Simplify the expression by following steps: - step0: Solution: \(\frac{x^{3}}{2}-3\times \frac{1}{x^{2}}-2x^{3}-x^{\frac{3}{2}}\) - step1: Multiply the terms: \(\frac{x^{3}}{2}-\frac{3}{x^{2}}-2x^{3}-x^{\frac{3}{2}}\) - step2: Reduce fractions to a common denominator: \(\frac{x^{3}\times x^{2}}{2x^{2}}-\frac{3\times 2}{x^{2}\times 2}-\frac{2x^{3}\times 2x^{2}}{2x^{2}}-\frac{x^{\frac{3}{2}}\times 2x^{2}}{2x^{2}}\) - step3: Reorder the terms: \(\frac{x^{3}\times x^{2}}{2x^{2}}-\frac{3\times 2}{2x^{2}}-\frac{2x^{3}\times 2x^{2}}{2x^{2}}-\frac{x^{\frac{3}{2}}\times 2x^{2}}{2x^{2}}\) - step4: Transform the expression: \(\frac{x^{3}\times x^{2}-3\times 2-2x^{3}\times 2x^{2}-x^{\frac{3}{2}}\times 2x^{2}}{2x^{2}}\) - step5: Multiply the terms: \(\frac{x^{5}-3\times 2-2x^{3}\times 2x^{2}-x^{\frac{3}{2}}\times 2x^{2}}{2x^{2}}\) - step6: Multiply the numbers: \(\frac{x^{5}-6-2x^{3}\times 2x^{2}-x^{\frac{3}{2}}\times 2x^{2}}{2x^{2}}\) - step7: Multiply the terms: \(\frac{x^{5}-6-4x^{5}-x^{\frac{3}{2}}\times 2x^{2}}{2x^{2}}\) - step8: Multiply the terms: \(\frac{x^{5}-6-4x^{5}-2x^{\frac{7}{2}}}{2x^{2}}\) - step9: Subtract the terms: \(\frac{-3x^{5}-6-2x^{\frac{7}{2}}}{2x^{2}}\) - step10: Rewrite the fraction: \(-\frac{3x^{5}+6+2x^{\frac{7}{2}}}{2x^{2}}\) - step11: Simplify: \(-\frac{3x^{5}+6+2x^{3}\sqrt{x}}{2x^{2}}\) The simplified form of the given function \( f(x) = \frac{x^{3}}{2} - 3x^{-2} - 2x^{3} - x^{3/2} \) is \( -\frac{3x^{5}+6+2x^{3}\sqrt{x}}{2x^{2}} \).