Question

How would the fraction 5/1-sort 3. Be written if it’s denominator is rationalized using difference of squares?

Answer 1

Answer:

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

Option A is the correct option.

Solution,

Multiply and divide by its conjugate.

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

hope this helps...

Good luck on your assignment..