How do you rationalize this equation?

Question

14-sqrtx/sqrtx

Answer 1

(14 - √x) / √x
√x (14 - √x) / x
(14√x - x) / x

Answer 2

First of all, this isn't an equation.

An equation has to consist of a series of expressions that equal something.

You have an expression...this is terminology from my era, you may call it something else today.

But in any case, the best I can say is to multiply top and bottom of this fraction by sqrt x.

Assuming that what you started with is (14-sqrtx)/sqrtx, what you end up with is: (14sqrtx-x)/x.

This is rationalized to the extent that there is no radical in the denominator.

There is no obvious further simplifcation that you can do, beyond breaking it our as (14sqrtx/x) -1, but I don't like that form as well.

Answer 3

If you meant (14 - sqrt(x))/sqrt(x), then the denominator of this expression can be rationalized by multiplying the numerator and denominator by sqrt(x), to yield (14sqrt(x) - x)/x, which is the same as 14sqrt(x)/x - 1.

If you meant 14 - sqrt(x)/sqrt(x), then the answer is just 13.

Regardless of which case you meant, x cannot equal zero.

Answer 4

If there are no parenthesis, then the sqrts cancel each other.

Its 14-1

Answer 5

(14 - rtx)(14 - rtx)

196 -28rtx + x
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x