A Shortcut when Simplifying Rational Expressions

Simplifying rational expressions is a fundamental concept in algebra that involves reducing complex fractions or rational functions to their simplest form. Rational expressions are mathematical expressions that consist of polynomial functions in the numerator and denominator, separated by a fraction bar. The goal of simplification is to eliminate common factors and reduce the expression to its most compact and manageable form.

By simplifying rational expressions, you make them easier to work with and evaluate. This simplification process is particularly valuable when solving equations, finding asymptotes, or analyzing the behavior of functions, as it allows for a clearer understanding of the underlying mathematical relationships. It's an essential skill for anyone studying algebra, calculus, or other advanced mathematics.

[universalalgorithm]

What if p=q? Would that give you an indeterminate form or would that number simply not exist?

[nilsalmgren]

So what he is saying is that if you subtract two numbers in the opposite order, you get the same number but opposite sign. Any number divided by itself is one and dividing a positive and a negative is negative...hence the answer will always be negative 1 as long as the two numbers are the same....