Question

How would the fraction

Answer 1

Answer:

A. ${-\frac{5+5\sqrt 3 }{2}}$

Step-by-step explanation:

Please wait for more explanation:

$\frac{5}{1-\sqrt 3}= \frac{5}{1-\sqrt 3}\times \frac{1+\sqrt 3}{1+\sqrt 3}\\\\= \frac{5(1+\sqrt 3) }{1^2 -(\sqrt 3) ^2}\\\\= \frac{5+5\sqrt 3 }{1 -3}\\\\= \frac{5+5\sqrt 3 }{-2}\\\\=\huge\purple {\boxed {-\frac{5+5\sqrt 3 }{2}}}$

Answer 2

The differences of squares:  a² - b² = (a - b)(a + b)

at denominator we have:  a - b  and we want:  a² - b²

so we need to multiply by (a+b)  {both denominator and nominator!}

$\dfrac5{1-\sqrt3}=\dfrac{5(1+\sqrt3)}{(1-\sqrt3)(1+\sqrt3)}=\dfrac{5(1+\sqrt3)}{1^2-(\sqrt3)^2}=\dfrac{5+5\sqrt3}{1-3}=\dfrac{5+5\sqrt3}{-2}=-\dfrac{5+5\sqrt3}{2}$

The answer is  A