Adding and subtracting rational expressions 6

The Adding and subtracting rational expressions 6 exercise appears under the Algebra II Math Mission and Mathematics III Math Mission. This exercise practices work with rational expressions that need to be combined by addition and subtraction.

Types of Problems

There is one type of problem in this exercise:

1. Combine the rational expressions: This problem has the sum or difference of some rational expressions. The user is asked to combine the rational expressions and write the answer in the space provided.

   

   Combine the rational expressions

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 is to factor the denominators, make common denominators, add or subtract as requested, factor and simply as possible.
2. The numerator should be expanded and like terms collected.
3. The denominator may be left in a factored form and still be accepted.
4. Like terms and factors do need to be reduced from the top and bottom.
5. On this one, sixth in the series, the denominators are different and are binomial. There is more need to be careful with finding the common denominator and distributing correctly.

Real-life Applications

1. Rational expressions and equations appear often in work rate word problems.
2. Rational expressions and equations also can occur in ${\text{distance}=\text{rate}\times\text{time}}$ problems.