Learn how to solve simplification of algebraic fractions problems step by step online. Find the limit of (x^3-27)/(x^2-9) as x approaches 3. Factor the difference of cubes: a^3-b^3 = (a-b)(a^2+ab+b^2). If we directly evaluate the limit \lim_{x\to3}\left(\frac{\left(x-3\right)\left(x^2+3x+9\right)}{x^2-9}\right) as x tends to 3, we can see that it gives us an indeterminate form. We can solve this limit by applying L'Hôpital's rule, which consists of calculating the derivative of both the numerator and the denominator separately. After deriving both the numerator and denominator, and simplifying, the limit results in.

Find the limit of (x^3-27)/(x^2-9) as x approaches 3