A technician is evaluating an electrical circuit where the total resistance is modeled by the complex rational expression $\frac{n-\frac{4n}{n+5}}{\frac{1}{n+5}+\frac{1}{n-5}}$. To simplify this using the division method, the technician first simplifies the denominator of the main fraction. According to the procedure for this specific expression, which of the following is the correct simplified form of the denominator, $\frac{1}{n+5}+\frac{1}{n-5}$?

A student is asked to simplify the complex rational expression $\frac{n-\frac{4n}{n+5}}{\frac{1}{n+5}+\frac{1}{n-5}}$ by writing it as a division problem. Arrange the following steps in the correct chronological order according to this specific method.

A manufacturing engineer is simplifying the complex rational expression $\frac{n-\frac{4n}{n+5}}{\frac{1}{n+5}+\frac{1}{n-5}}$ to model the heat dissipation in a new component design. To use the 'Writing as Division' method, the engineer must first simplify the numerator and denominator separately. Match each component of this simplification process with its correct mathematical representation for this specific formula.

Numerator Simplification in Complex Rational Expressions

A data analyst is auditing a formula used to calculate a normalized performance metric, represented by the complex rational expression $\frac{n-\frac{4n}{n+5}}{\frac{1}{n+5}+\frac{1}{n-5}}$. When following the procedure to simplify this expression by writing it as division, the expression eventually becomes $\frac{n(n+1)(n+5)(n-5)}{2n(n+5)}$. At this stage, the common factors that are divided out from both the numerator and the denominator are $n$ and ______.