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.
