Question

The limit of (2*x^(2)-x-1)/(2-sqrt(x^(2)+3)) when x approaches 1. Or, simply, how do I simplify (2*x^(2)-x-1)/(2-sqrt(x^(2)+3)). Without L'Hospital's rule.

Answer 1

multiply both sides of the fraction by \[2+\sqrt{x^2 +3}\] then cancel common factors after expanding the denominator ONLY.

Answer 2

\[\frac{(2x ^{2}-x-1)(2+\sqrt{x^2+3})} {1-x^2}\] is what I should end up with, right?

Answer 3

What then?

Answer 4

factor (2x^2-x-1) and (1-x^2), you should be able to cancel terms that cause the numerator and denominator to become 0

Answer 5

I end up with 6. Is that right?