Respuesta :
Let us rewrite the given expression:
[tex]\frac{1}{1+\sqrt{3}}[/tex]
Now in this case we have to rationalise the denominator.
So we multiply and divide by 1 - √3
[tex]\frac{1}{1+\sqrt{3}}*\frac{1-\sqrt{3}}{1-\sqrt{3}}[/tex]
The denominator can be simplified using the property:
[tex](a+b)(a-b)=a^{2}-b^{2}[/tex]
[tex]\frac{1-\sqrt{3}}{1^{2}-(\sqrt{3})^{2}}[/tex]
So finally on simplifying we will get:
[tex]\frac{1-\sqrt{3}}{-2}[/tex]
Answer:
D
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 the 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
