Question

The question is this: Rationalize the denominator and simplify.

Answer 1

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Answer:

  $\dfrac{20+5\sqrt{3}}{13}$

Step-by-step explanation:

Multiply numerator and denominator by the "conjugate" of the denominator.

  $\dfrac{5}{4-\sqrt{3}}=\dfrac{5(4+\sqrt{3})}{(4-\sqrt{3})(4+\sqrt{3})}=\dfrac{20+5\sqrt{3}}{4^2-(\sqrt{3})^2}=\boxed{\dfrac{20+5\sqrt{3}}{13}}$

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This is done in different scenarios in order to take advantage of the factoring of the difference of squares. Square root terms and imaginary terms in the denominator can be eliminated in this way.

  a² - b² = (a -b)(a +b)