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

The fraction 5/(1-√3) is rationalized by multiplying the numerator and denominator by the conjugate 1+√3, which simplifies to (5+5√3) / -2, corresponding to answer option d. 5-5√3 / -2.

Step-by-step explanation:

To rationalize the denominator of the fraction 5/(1-√3), we multiply the numerator and denominator by the conjugate of the denominator. Here's the step-by-step process:

• Identify the conjugate of 1-√3, which is 1+√3.
• Multiply the numerator and denominator by 1+√3 to rationalize the denominator.
• The multiplication gives us (5 * (1+√3)) / ((1-√3) * (1+√3)).
• Use the difference of squares formula to simplify the denominator to 1 - (√3)^2, which equals 1 - 3 or -2.
• The numerator simplifies to 5 + 5√3.
• The final rationalized fraction is (5+5√3) / -2.

The correct answer from the options provided is d. 5-5√3 / -2.