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5Question: Rationalize the denominator of $\displaystyle rac{3}{\sqrt{7} - \sqrt{2}}$.To rationalize the denominator, we multiply both numerator and denominator by the conjugate of the denominator, which is $\sqrt{7} + \sqrt{2}$:Now simplify the denominator using the identity $(a - b)(a + b) = a^2 - b^2$:rac{3(\sqrt{7} + \sqrt{2})}{5}oxed{ rac{3(\sqrt{7} + \sqrt{2})}{5}}Question: Expand the product $(2x - 3y)(x^2 + 4xy - 5y^2)$.We apply the distributive property to expand the product:2x(x^2 + 4xy - 5y^2) = 2x^3 + 8x^2y - 10xy^2-3y(x^2 + 4xy - 5y^2) = -3x^2y - 12xy^2 + 15y^3$2x^3$