Limiting x^2/(x-1) as x Approaches 1 from the Left

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Homework Statement

Find the limit of x^2/(x-1) as x goes to 1 from the left.

Homework Equations

The Attempt at a Solution

It doesn't seem I can factor anything, but could I assume that since the numerator is a constant and the denomination is going to be negative because it's <1 then it's going to negative infinity? Is there anyway to show this algebraically? Thanks.

 

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Homework Statement

Find the limit of x^2/(x-1) as x goes to 1 from the left.

Homework Equations

The Attempt at a Solution

It doesn't seem I can factor anything, but could I assume that since the numerator is a constant and the denomination is going to be negative because it's <1 then it's going to negative infinity? Is there anyway to show this algebraically? Thanks.

You are correct.

$$\frac{x^2}{1-x} = \frac{x^2 -1}{1-x} + \frac{1}{1-x}$$

The limit as x-> $$1^{-}$$ of $$\frac{x^2 -1}{1-x}$$ is 2.
This
$$\frac{1}{1-x}$$ one does not exist.