Objective: Find common denominators of rational expressions and add and subtract rational expressions that contain unlike denominators.
Like adding and subtracting fractions that do not contain like denominators, adding and subtracting rational expressions that do not contain like denominators requires the additional step of rewriting equivalent expressions so that they share a common denominator. With rational expressions, the process for finding common denominators can be more complex. To find the least common denominator, first factor the polynomial in each denominator and then multiply each expression with the missing factor(s). Once the equivalent expressions are written, you can add or subtract the numerators and simplify like we learned in the previous lesson. Watch the video to see this process performed.
Some denominators may contain polynomials that are opposites of each other. For example, x-3 and 3-x are considered opposites because if you multiplied either binomial by -1 they would be the same. If we notice that rational expressions have denominators that are opposites, we can multiply the expression by -1/-1 to make the opposites the same. This will help us find common denominators more easily. Watch the video to see how to add and subtract when denominators contain opposites.
Complete the worksheet attachment below and then check your answers using the solutions attachment. Once you have completed these exercises, click the link to advance to the next lesson.