Step 1: Rewrite the expression with the denominator in exponent form. The square root of $x$ can be written as $x^{1/2}$. $$y = \frac{4x^2 + 3x - 2}{x^{1/2}}$$ Step 2: Divide each term in the numerator by the denominator. $$y = \frac{4x^2}{x^{1/2}} + \frac{3x}{x^{1/2}} - \frac{2}{x^{1/2}}$$ Step 3: Simplify each term using the exponent rule $\frac{a^m}{a^n} = a^{m-n}$. For the first term: $$4x^{2 - 1/2} = 4x^{4/2 - 1/2} = 4x^{3/2}$$ For the second term: $$3x^{1 - 1/2} = 3x^{2/2 - 1/2} = 3x^{1/2}$$ For the third term: $$2x^{-1/2}$$ Step 4: Combine the simplified terms. $$y = 4x^{3/2} + 3x^{1/2} - 2x^{-1/2}$$ The simplified expression is: $$\boxed{y = 4x^{3/2} + 3x^{1/2} - 2x^{-1/2}}$$ Send me the next one 📸