How to rationalize the numberator?

  • Thread starter dtcool2003
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In summary, the user is looking for help with rationalizing the numerators of two equations involving square roots. They are advised to use the conjugate of the square root terms to eliminate them from the numerator and then simplify the resulting equation.
  • #1
dtcool2003
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Here is the question: the square root of X minus 3, but the 3 is not under the square root divided by x-9? also another question: the square root of X minus 2, but the 2 is not under the square root divided by 4-x? anyone can help me?
 
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  • #2
How to rationalize the numerator?

Here is the question: sqrt(x) - 3/ x-9 ? also another question: sqrt(x) -2/ 4-x ? anyone can help me? Thanks
 
Last edited:
  • #3
So you mean sqrt(x)/(x-9) - 3/(x-9)?
 
  • #4
No

no I mean, sqrt(x) - 3/ x-9 ? also another question: sqrt(x) -2/ 4-x ? anyone can help me? Thanks and I need to rationalize the numerator
 
  • #5
Nope, i guess he means

[tex]\frac{\sqrt{x} -3}{x-9} [/tex] and [tex] \frac{\sqrt{x} -2}{4-x} [/tex]

When rationalizing, remember that [itex]a^2 - b^2 \equiv (a+b)(a-b) [/itex]. So take [/itex] a=\sqrt{x} [/itex]. What is 'b' equal to ?
 
  • #6
yeah

those are the right equations u just put up, but i don't know how to rationalize those equations?
 
  • #7
yeah

I got x-9/ x-9sqrt(x) + 3x - 27 is that right?
 
  • #8
[tex]\frac{\sqrt{x}-3}{x^2- 9}[/tex]
That it?

Use (a- b)(a+ b)= a2- b2: multiply both numerator and denominator by [itex]\sqrt{3}+ 3[/itex] and the squareroot will disappear from the numerator. It will, of course, show up in the denominator.

For the second, assuming you have a fraction with [itex]\sqrt{x}- 2[/itex] in either numerator or denominator, multiply both numerator and denominator by [itex]\sqrt{x}+ 2[/itex]
 
  • #9
This is not a "Linear and Abstract Algebra" question and it was also posted in the "General Math" section so I am merging the two threads in that section.
 
  • #10
[tex] \frac {\sqrt{x}-3}{x-9} [/tex]

Multiply:
Both [tex] {x-9} [/tex] and [tex] {\sqrt{x}-3}[/tex]

By the conjugate of [tex]{\sqrt{x}-3}[/tex] which is [tex]{\sqrt{x}+3}[/tex].

[tex] \frac {\sqrt{x}-3( \sqrt{x}+3)} {x-9( \sqrt{x}+3)}[/tex]

From here, you should be able to do some algebra, to rationalize the numerator. Do you know what a conjugate is, and why it is used? That might be your issue with not understanding it.
 

FAQ: How to rationalize the numberator?

How do I rationalize the numerator of a fraction?

Rationalizing the numerator of a fraction involves manipulating the fraction in a way that eliminates any radicals or imaginary numbers in the numerator. This is typically done by multiplying the fraction by a suitable form of 1, such as the conjugate of the numerator's radical.

Why is it important to rationalize the numerator?

Rationalizing the numerator allows for easier calculation and comparison of fractions. It also helps to simplify the fraction and make it easier to work with in further calculations.

Can I rationalize the numerator of any fraction?

Yes, the process of rationalizing the numerator can be applied to any fraction with a radical or imaginary number in the numerator. However, it may not always be necessary or beneficial to do so.

Are there any tricks to quickly rationalize the numerator?

There are a few common techniques that can be used to quickly rationalize the numerator, such as multiplying by the conjugate or using the rationalizing factor formula. However, the best approach may vary depending on the specific fraction and its components.

What are some common mistakes to avoid when rationalizing the numerator?

One common mistake is forgetting to rationalize the denominator as well, which is necessary in order to maintain the value of the fraction. Another mistake is incorrectly applying the rationalizing techniques, which can lead to incorrect results. It is important to double check the steps and answer when rationalizing the numerator to avoid these errors.

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