Question

how would the fraction 5÷1-√(3 be rewritten if it's denominator is rationalized using difference of squares

Answer 1

-5(1 + √3)/2

Explanation:

To rationalize 5÷1-√3, we multiply both the numerator and the denominator by the conjugate of 1 - √3 = 1 + √3.

So 5 ÷ (1 - √3) = 5/(1 - √3), we multiply by the conjugate of the denominator, we have

5/(1 - √3) × (1 + √3)/(1 + √3) = 5(1 + √3)/[(1 - √3) × (1 + √3)]

= 5(1 + √3)/(1² - (√3)²)

= 5(1 + √3)/(1 - 3)

= 5(1 + √3)/-2

= -5(1 + √3)/2