Question

How would the fraction 5/1-√3 be rewritten if its denominator is rationalized using difference of squares

A. - (5+5√(3))/2
B. (5-5√(3))/2
C. (5-5√(3))/-2
D. (5+5√(3))/2 ​

Answer 1

To rationalize the denominator of 5/(1-√3), multiply the numerator and denominator by (1+√3). The result is - (5+5√(3))/2 after applying difference of squares and simplifying. Option A is correct.

Step-by-step explanation:

To rationalize the denominator of the fraction 5/(1-√3), we need to eliminate the square root from the denominator. We can do this by multiplying the numerator and denominator by the conjugate of the denominator, which in this case is (1+√3). The conjugate is chosen because when we multiply a binomial by its conjugate, we get the difference of squares, which eliminates the square root from the denominator.

Here are the steps to rationalize the denominator:

4. Write down the original fraction: 5/(1-√3).
8. Multiply both the numerator and the denominator by the conjugate of the denominator: (1+√3).
12. Apply the difference of squares in the denominator: (1-√3)(1+√3)=1^2-(√3)^2=1-3=-2.
16. Multiply through the numerator: 5(1+√3).
20. Simplify the resulting expression: (5+5√3)/-2 or -1/2(5+5√3), which is equivalent to - (5+5√(3))/2.

Therefore, the fraction 5/(1-√3) when rationalized using the difference of squares yields - (5+5√(3))/2, which matches option A.