Last week’s introduction to Rational Expressions showed us expressions with monomial denominators. Week 13 gave us a glimpse of expressions with binomial and trinomial denominators. The best strategy to determine the common denominator for any expression is to factor all the known denominators. After that, write the product of the different factors with the greatest exponent of each factor. Let’s try question 10c (on page 568) to fully understand this concept.
First of all, factor all trinomials in both numerators and denominators.
From here, we can see (in the denominators) the non-permissible values are: 
Now, we simplify before finding the common denominator.
After that, the common denominator is (
Now, we must simplify.
In the next unit, we learned how to solve equations involving rational expressions. Similar to what we learned in the previous unit, the common denominator is needed. Question 10b (on page 585) is a perfect example.
Next, we must factor the denominator.
The common denominator is 2(
After that, we multiple each side of the equation by 2(
Distribute and put all like terms to one side of the equation and finally, solve.
Because -3 is a non-permissible value of the variable,
(Another way of looking at this process is “cross multiplying the numerator to the opposite denominator” and vice versa. The simplifying method is exactly the same as shown above.)
