Multiplying and dividing rational expressions 5

The  exercise appears under the Algebra II Math Mission. This exercise practices work with rational expressions that need to be combined by multiplication and division, and also basic domain considerations.

Types of Problems
There is one type of problem in this exercise:


 * 1) Combine the rational expressions: This problem has the product or quotient of some rational expressions. The student is asked to combine the rational expressions as asked and write the answer in the space provided and also describe the domain where the simplification is valid.Madre4-1.png

Strategies
As with most work with rational expressions, knowledge and comfort with fractions are important to ensuring success on this exercise.
 * 1) The general process to combine rational expressions here is to factor the numerators and denominators, multiply or divide as requested, and then reduce common factors from top and bottom as possible.
 * 2) The denominator should be left in a factored form with GCFs factored out, especially from the denominator.
 * 3) Like terms and factors do need to be reduced from the top and bottom.
 * 4) On this one, fourth in the series,  advanced factoring techniques are needed in addition to the distributive property. For example, quadratic factoring, difference of squares and some basic cubic factoring can appear. Be sure to reduce as needed
 * 5) Numbers which cause division by zero must be excluded from the domain of the simplification.

Real-life Applications

 * 1) Rational expressions and equations appear often in work rate word problems.
 * 2) Rational expressions and equations also can occur in distance=rate*time problems.