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Rationalize the Denomiantor

by Charles
(Indiana)











































“rewrite the expression so there are no radicals in the denominator”.

(-5x^2)/sqrt(7x+9)

Since there is only one term in the denominator which is under a square root sign, that radical can be removed by multiplying the original expression by a fraction where: both the numerator and denominator are equal to the denominator of the original expression.

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Mar 02, 2011
Rationalize the Denominator
by: Staff

The question:

(-5x^2)/sqrt(7x+9)


The answer:

Rationalizing the Denominator is the standard way of simplifying fractions containing radicals in the denominator.

Rationalizing the denominator means to “rewrite the fraction so there are no radicals in the denominator”.

Your problem:
(-5x^2)/sqrt(7x+9)


“IF” we could multiply the sqrt(7x+9) by itself the sqrt sign in the denominator would disappear:

sqrt(7x+9)* sqrt(7x+9) = 7x+9


However, the real question is how to employ this technique without altering the value of the original fraction: (-5x^2)/sqrt(7x+9)


The answer is to multiply the original fraction by another fraction which is equal to 1.

[(-5x^2)/sqrt(7x+9)]*1 = (-5x^2)/sqrt(7x+9), the original fraction

sqrt(7x+9)/sqrt(7x+9) = 1


Therefore, we can substitute sqrt(7x+9)/sqrt(7x+9) for 1

[(-5x^2)/sqrt(7x+9)]*1 = (-5x^2)/sqrt(7x+9), the original fraction

[(-5x^2)/sqrt(7x+9)]* [sqrt(7x+9)/sqrt(7x+9)] = (-5x^2)/sqrt(7x+9), the original fraction


= [(-5x^2)* sqrt(7x+9)]/[sqrt(7x+9)*sqrt(7x+9)]

Note that the denominator now = [sqrt(7x+9)*sqrt(7x+9)]

= (7x+9)


The original fraction can now be rewritten:

= [(-5x^2)* sqrt(7x+9)]/(7x+9)


The final answer is: [(-5x^2)* sqrt(7x+9)]/(7x+9)



Thanks for writing.


Staff
www.solving-math-problems.com



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