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\[\frac{ x ^{2}-\sqrt{x} }{ 1-\sqrt{x} }\]

x-->1

Do you know how to solve this?

you may try rationalizing, both numerator and denom separately..

but how can i do that? do first the denomitador and then de numerator or both at the same time?

doesnt matter..

any order you prefer..

??

The limit is -3.

you may rationalize either denom or nume first,,order wont matter..

Use L'Hospital Rule

i get 3x

yeep, i know the limit, but what i dont, is how to find it

Just take the derivative of the top, and then take the derivative of the bottom,

It is -3

Then plug in 1 for x and that will give you the limit.

:/

Just multiply top and bottom by conjugates then.

no,

What you want to do is rationalize one side.

So, just multiply top and bottom by 1+sqrt(x)

You should get 1-x for the bottom

you would have parenthesis around x^2 and sqrt x

mm yes so what can i do next?

I am not sure actually you still have on the denominator 1-1 which is still dividing by a zero

your limit does not exist?

\(\huge\frac{ (x ^{2}-\sqrt{x})(1+\sqrt{x}) }{1-x }\times \frac{x^2+\sqrt x}{x^2+\sqrt x}\)

x^4-x = x(x^3-1) = x(x-1)(x^2x+x+1)

put x=1 after cancelling 1-x

divide both num and dem by x^2..