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IRISSAK [1]
3 years ago
12

How would the fraction

Mathematics
2 answers:
Bumek [7]3 years ago
8 0

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}}} \\

aleksley [76]3 years ago
5 0

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

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