Learn how to solve problems step by step online. Find the limit of (x^2-(a+1)xa)/(x^3-a^3) as x approaches infinity. Factor the difference of cubes: a^3-b^3 = (a-b)(a^2+ab+b^2). Simplify \sqrt[3]{\left(a^3\right)^{2}} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 3 and n equals \frac{2}{3}. Multiply the single term x^2+xa+a^{2} by each term of the polynomial \left(x-a\right). Multiply the single term x by each term of the polynomial \left(x^2+xa+a^{2}\right).

Find the limit of (x^2-(a+1)xa)/(x^3-a^3) as x approaches infinity