Exercise
$f\left(x\right)=\frac{x^2}{x^3+a^3}$
Step-by-step Solution
Learn how to solve problems step by step online. Simplify the expression f(x)=(x^2)/(x^3+a^3). Factor the sum or difference of cubes using the formula: a^3\pm b^3 = (a\pm b)(a^2\mp ab+b^2). Simplify \sqrt[3]{x^3} 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{1}{3}. Simplify \sqrt[3]{a^3} 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{1}{3}. Simplify \sqrt[3]{\left(x^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}.
Simplify the expression f(x)=(x^2)/(x^3+a^3)
Final answer to the exercise
$f\left(x\right)=\frac{x^2}{\left(x+a\right)\left(x^{2}-xa+a^{2}\right)}$