Given the function \( h(x) = \frac{3x + 5}{\sqrt{2x + 1}} \), rationalize the denominator and simplify.
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- \[(3x - 2)^2 = (3x)^2 - 2(3x)(2) + (2)^2.\]
- \[ = 9x^2 - 12x + 4. \]
- The square of \( (3x - 2) \) is \(\boxed{9x^2 - 12x + 4}\).**Question:
- To rationalize the denominator of \( h(x) = \frac{3x + 5}{\sqrt{2x + 1}} \), we multiply both the numerator and the denominator by \( \sqrt{2x + 1} \) to eliminate the square root in the denominator:
- h(x) = \frac{3x + 5}{\sqrt{2x + 1}} \cdot \frac{\sqrt{2x + 1}}{\sqrt{2x + 1}} = \frac{(3x + 5) \sqrt{2x + 1}}{2x + 1}
- The rationalized form is:
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