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You multiply the numerator and the denominator by the same expression - and do it in such a way that the denominator becomes rational.Example 1: The denominator is square root of 5, which I will call root(5). If you multiply top and bottom by root(5), the denominator will become rational.
Example 2: The denominator is root(2) + root(3). If you multiply top and bottom by root(2) - root(3), then the denominator will become rational.
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Fran- You multiply both, the numerator and the denominator, of the fraction by the complex conjugate of the denominator. The complex conjugate of (x + iy) is (x - iy). Thus (u + iv)/(x + iy) =[(u + iv)*(x - iy)]/[(x + iy)*(x - iy)] and the denominator is then x2 -ixy + ixy - i2y2 = x2 + y2 which is real but it may or may not be rational.
- If this denominator is irrational, you can rationalise is by a similar process, using the irrational conjugate. For [p + sqrt(q)], it is [p - sqrt(q)].
There are denominators which cannot be rationalised. For example 3/pi.
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Can you use conjugates to rationalize the denominator even when the denominator contains two radical terms?
Yes. The original denominator and its conjugate will form the factors of a Difference of Two Squares (DOTS) and that will rationalise the denominator but only if the radicals are SQUARE roots.
To rationalize a denominator that has more than one term you multiply the fraction by where B is the conjugate of the denominator.?
Yes, that is correct.
What is the importance of the conjugate in rationalizing the denominator of a rational expression that has a radical expression in the denominator?
To eliminate the radical in the denominator.
Common denominator for numbers 3 5 7?
1 is the only common denominator.
What is true about both the numerator and denominator of rational expressions?
Both the numerator and denominator are polynomials
