Respuesta :

9514 1404 393

Answer:

  -(5√7 +9√35)/380

Step-by-step explanation:

The denominator is made rational by multiplying numerator and denominator by the conjugate of the denominator.

  [tex]\dfrac{\sqrt{7}}{5-9\sqrt{5}}=\dfrac{\sqrt{7}}{5-9\sqrt{5}}\cdot\dfrac{5+9\sqrt{5}}{5+9\sqrt{5}}=\dfrac{5\sqrt{7}+9\sqrt{35}}{5^2-9^2\cdot5}=\boxed{-\dfrac{5\sqrt{7}+9\sqrt{35}}{380}}[/tex]

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Additional comment

This process takes advantage of the factoring of the difference of squares:

  a² -b² = (a -b)(a +b)

The method is used to eliminate complex numbers and square roots from denominators.

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