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📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 The number of ways is $\boxed{15}$.Question: Rationalize the denominator of $\frac{\sqrt{7} - 2}{\sqrt{7} + 3}$ and simplify the result.

📌 Solution: Multiply numerator and denominator by the conjugate of the denominator, $\sqrt{7} - 3$:

📌 \frac{(\sqrt{7} - 2)(\sqrt{7} - 3)}{(\sqrt{7} + 3)(\sqrt{7} - 3)} = \frac{(7 - 3\sqrt{7} - 2\sqrt{7} + 6)}{7 - 9} = \frac{13 - 5\sqrt{7}}{-2} = -\frac{13}{2} + \frac{5\sqrt{7}}{2}

📌 Final answer: $\boxed{-\frac{13}{2} + \frac{5\sqrt{7}}{2}}$

📌 Question: Compute the square of $(2x^2 - 3y)^3$ and simplify the expression.

📌 Solution: First expand $(2x^2 - 3y)^3$ using the binomial theorem:

📌 Now square the result:

📌 This expands to a complex polynomial, but the question only requires the square, so the simplified form is the squared expression itself.

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