Final answer to the problem
$f\left(x\right)=\frac{x^{4}-1}{\left(x-3\right)\left(2x^3-3x\right)}$
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Step-by-step Solution
Learn how to solve factor by difference of squares problems step by step online. Simplify the expression f(x)=((x^2+1)/(x-3))/((2x^3-3x)/(x^2-1)). We can simplify the quotient of fractions \frac{\frac{x^2+1}{x-3}}{\frac{2x^3-3x}{x^2-1}} by inverting the second fraction and multiply both fractions. The sum of two terms multiplied by their difference is equal to the square of the first term minus the square of the second term. In other words: (a+b)(a-b)=a^2-b^2.. Simplify \left(x^2\right)^2 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 2 and n equals 2. Multiply 2 times 2.
Final answer to the problem
$f\left(x\right)=\frac{x^{4}-1}{\left(x-3\right)\left(2x^3-3x\right)}$
