Respuesta :

SaniShahbaz

Answer:

4th option

Step-by-step explanation:

The given expression is:

[tex]\frac{1}{1+\sqrt{3}}[/tex]

In order to simplify this expression we have to multiply and divide it with the conjugate of the denominator i.e multiply and divide the entire expression with [tex]1-\sqrt{3}[/tex], as shown below:

[tex]\frac{1}{1+\sqrt{3}}\\=\frac{1}{1+\sqrt{3}} \times \frac{1-\sqrt{3}}{1-\sqrt{3}}\\=\frac{1-\sqrt{3}}{(1)^{2}-(\sqrt{3})^{2}}\\\\ =\frac{1-\sqrt{3}}{1-3}\\\\ =\frac{1-\sqrt{3}}{-2}\\\\ =\frac{-1(1-\sqrt{3})}{2}\\\\ =\frac{-1+\sqrt{3}}{2}[/tex]

Thus, 4th option gives the correct answer.

abidemiokin

Answer:

The right option is D -1+√3/2

Step-by-step explanation:

To find the quotient of the sure function 1/1+√3, we will rationalize the surd function by multiplying the numerator and the denominator of the surd by the conjugate of its denominator.

Given he denominator to be 1+√3, the conjugate of 1+√3 is 1-√3

Multiplying by 1-√3 will result in the following;

1/1+√3×1-√3/1-√3

= 1-√3/(1+√3)(1-√3)

= 1-√3/1-√3+√3-√9

= 1-√3/1-√9

= 1-√3/1-3

= 1-√3/-2

= -(1-√3)/2

= -1+√3/2

The right option is D -1+√3/2

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