How do you rationalize the denominator and simplify (x-3)/(sqrtx-sqrt3)?

2 Answers
Douglas K.
Sep 26, 2016

To rationalize a denominator in the form of sqrta - sqrtb, you multiply the fraction by 1 in the form (sqrta + sqrtb)/(sqrta + sqrtb)

Explanation:

The reason for doing this practice comes from general form for factoring binomials that contain the difference two squares:

a^2 - b^2 = (a - b)(a + b)

Returning to the given fraction, we multiply by 1 in form (sqrtx + sqrt3)/(sqrtx + sqrt3)

(x - 3)/(sqrtx - sqrt3)(sqrtx + sqrt3)/(sqrtx + sqrt3) =

((x - 3)(sqrtx + sqrt3))/(x - 3) =

sqrtx + sqrt3

Nityananda
Sep 26, 2016

sqrt x + sqrt 3

Explanation:

divide the Numerator and denominator by sqrtx + sqrt 3.
we get, ( x - 3)/(sqrt x - sqrt 3) * (sqrt x + sqrt 3)/(sqrt x + sqrt 3)
= [(x - 3)(sqrt x + sqrt 3)]/[(sqrt x)^2 - (sqrt 3)^2] = [(x - 3)(sqrt x + sqrt 3)]/(x - 3) = sqrt x + sqrt 3

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