Question

How would the fraction 5/1-√3. Be written if it’s 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), resulting in the expression 5-5√3/2, which corresponds to choice d.

The fraction now has a rationalized denominator, and the correct expression is choice d. 5-5√3/2.

Step-by-step explanation:

To rationalize the denominator of the fraction 5/(1-√3), we want to eliminate the square root from the denominator. To do this, we will use the difference of squares formula, which states that (a+b)(a-b) = a2 - b2. Applying this to rationalize our denominator, we multiply both the numerator and the denominator by the conjugate of the denominator, which for 1 - √3 is 1 + √3.

Here's the step-by-step process:

1. Multiply the numerator and denominator by the conjugate of the denominator: (5 * (1+√3)) / ((1-√3)(1+√3))
2. Apply the difference of squares to the denominator: 5(1+√3) / (12 - (√3)2)
3. Simplify the denominator using the knowledge that √3 * √3 = 3: 5(1+√3) / (1 - 3)
4. The denominator simplifies to -2, and distribute the 5 in the numerator: (5+5√3) / -2