Week #13 – Rational Equations. this week, a mistake I made was dividing with Rational Equations.
The problem I solved incorrectly was:
Simplify the expression and determine any restrictions on the variable.
One mistake that often happens with these types of problems is rushing to simplify without considering the overall structure of the expression. Since this is a complex fraction, the best approach is to simplify the numerator and denominator separately before combining them.
For example, in the numerator:
This factoring step is easy to overlook if you’re not paying attention. It’s also important to find a common denominator before subtracting the fractions.
In my case, I tried subtracting the fractions right away without setting up the common denominators or properly organizing the expression. That led to confusion and the wrong answer.
Once everything is simplified carefully, the expression becomes easier to manage, and we can identify any values that would make the denominator zero. These are the restrictions:
