Adding and subtracting rational expressions 3

The  exercise appears under the Algebra II 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 three rational expressions. The student is asked to combine the rational expressions and write the answer in the space provided.Ratexp3-1.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 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, third in the series, the denominators of the expressions are the same, but there are binomials involved and potentially several different variables. Care needs to be taken with the distributive property, observing the correct like terms that can be combined, and reducing appropriately when called for.

Real-life Applications

 * 1) Rational expressions and equations appear often in work rate word problems