Respuesta :

Hrishii

Answer:

A. [tex] {-\frac{5+5\sqrt 3 }{2}}[/tex]

Step-by-step explanation:

Please wait for more explanation:

[tex] \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}}} \\[/tex]

The fraction 5/1-√3 can be rewritten if its denominator is rationalized using difference of squares as -5(1 + √3)/2.

What is simplification of an expression?

Usually, simplification involves proceeding with the pending operations in the expression.

Simplification usually involves making the expression simple and easy to use later.

To rationalize 5÷1-√3,  by the conjugate of 1 - √3 = 1 + √3.

So 5 ÷ (1 - √3) = 5/(1 - √3),

we multiply the expression by the conjugate of the denominator, we have,

5/(1 - √3) × (1 + √3)/(1 + √3)

= 5(1 + √3)/[(1 - √3) × (1 + √3)]

=  5(1 + √3)/(1² - (√3)²)

=  5(1 + √3)/(1 - 3)

= 5(1 + √3)/-2

= -5(1 + √3)/2

Learn more about factored form of an expression here:

https://brainly.com/question/1249625

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