# Question on lim x→1 (x − 5) / (x^2 + 2x − 4) ?

## Homework Statement

Determine whether the statement is true or false. lim x→1 (x − 5) / (x^2 + 2x − 4) = lim x→1 (x − 5) / lim x→1 (x^2 + 2x − 4)?

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## The Attempt at a Solution

I know that the right side of this equation and the left side have to equal each other in order for this to be true. On the right hand side the answer is 4. I don't know how to solve the left hand side because (x^2 + 2x − 4) cannot be factored.

SteamKing
Staff Emeritus
Homework Helper

## Homework Statement

Determine whether the statement is true or false. lim x→1 (x − 5) / (x^2 + 2x − 4) = lim x→1 (x − 5) / lim x→1 (x^2 + 2x − 4)?

[/B]

## The Attempt at a Solution

I know that the right side of this equation and the left side have to equal each other in order for this to be true. On the right hand side the answer is 4. I don't know how to solve the left hand side because (x^2 + 2x − 4) cannot be factored.
That's irrelevant. Can the limit of the LHS expression be evaluated without factoring the quadratic?