Question

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

Answer 1

What you would do is use the 'difference of two squares' principle to identify the binomial (two-term) expression that will multiply by (1 - √3) to give only a number as a rational number cannot be a surd.
However, you cannot simply multiply just the denominator as this would alter the value of the expression so what you have to do is multiply the expression by the fraction that is: 'found binomial expression' / 'found binomial expression', which is simply equivalent to 1 and so the value of the original expression will not be changed.
So, how do you find the 'binomial term':
All you have to do is invert the sign, so the binomial term will be:
(1 + √3)

So you now just multiply the original expression by (1 + √3)/ (1 + √3) and simplify of course.