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1 (2sqrt(7) + 3sqrt(3))(2sqrt(7) - 3sqrt(3))(2sqrt(7) + 3sqrt(3)) + 1 (2sqrt(7) - 3sqrt(3))(2sqrt(7) + 3sqrt(3))(2sqrt(7) - 3sqrt(3))

Mathematics

ScanSolve AI Answer

Answer

474\sqrt{7}

Step-by-step solution

2 steps

  1. Combine the numerators over the common denominator.

    1⋅(27+33)(27−33)(27+33)+1⋅(27−33)(27+33)(27−33)\frac{1 \cdot (2\sqrt{7} + 3\sqrt{3})}{(2\sqrt{7} - 3\sqrt{3})(2\sqrt{7} + 3\sqrt{3})} + \frac{1 \cdot (2\sqrt{7} - 3\sqrt{3})}{(2\sqrt{7} + 3\sqrt{3})(2\sqrt{7} - 3\sqrt{3})}

    Since the common denominator is 1, the expression simplifies to:

    (27+33)+(27−33)(2\sqrt{7} + 3\sqrt{3}) + (2\sqrt{7} - 3\sqrt{3})

  2. Simplify the expression by combining like terms.

    27+33+27−332\sqrt{7} + 3\sqrt{3} + 2\sqrt{7} - 3\sqrt{3} (27+27)+(33−33)(2\sqrt{7} + 2\sqrt{7}) + (3\sqrt{3} - 3\sqrt{3}) 47+04\sqrt{7} + 0 474\sqrt{7}
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