- #1

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I've been stumped on a basic question.

Show that:

[tex] \frac{{\sqrt x - \sqrt a }}{{x - a}} = \frac{1}{{\sqrt x + \sqrt a }} [/tex]

I've tried removing the radical sign, bringing the denominator up, etc...

Help?

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- Thread starter spynjr
- Start date

- #1

- 5

- 0

I've been stumped on a basic question.

Show that:

[tex] \frac{{\sqrt x - \sqrt a }}{{x - a}} = \frac{1}{{\sqrt x + \sqrt a }} [/tex]

I've tried removing the radical sign, bringing the denominator up, etc...

Help?

- #2

- 445

- 3

Hint: multiply by some form of one.

Answer: multiply by x^1/2 -a^1/2/x^1/2 -a^1/2 (which is one)

- #3

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I can see that it's correct numerically though.

Is that a general algebraic rule or can you get to it algebraically?

- #4

symbolipoint

Homework Helper

Education Advisor

Gold Member

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Maybe you could not read through the text straight-line-text form of the expression. See as

[tex] \[

\frac{{\sqrt x - \sqrt a }}{{\sqrt x - \sqrt a }}

\]

[/tex]

- #5

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Nonetheless I've figured out the way that makes most sense to me. Simply factor x-a which equals (sqrt(x)-sqrt(a))(sqrt(x)+sqrt(a)) (difference of two squares) then cancel (sqrt(x)-sqrt(a))

- #6

cristo

Staff Emeritus

Science Advisor

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Nonetheless I've figured out the way that makes most sense to me. Simply factor x-a which equals (sqrt(x)-sqrt(a))(sqrt(x)+sqrt(a)) (difference of two squares) then cancel (sqrt(x)-sqrt(a))

Well done: that's the way I would do it!

- #7

- 445

- 3

Woops, change those minus to plus haha.

Hint: multiply by some form of one.

Answer: multiply by x^1/2 -a^1/2/x^1/2 -a^1/2 (which is one)

Unlessn you apply it to the RH =P

Conjugates.

- #8

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- #9

epenguin

Homework Helper

Gold Member

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'Difference of two squares' is maybe a refrain to remember.

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