Adding, Subtracting, Multiplying, and Dividing Rational Expressions – Practice Problems

Having fun while studying, practice your skills by solving these exercises!

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Operations with rational expressions are essentially the same as operations with fractions. One is just dealing with polynomials instead of numbers in the numerator and denominator of the expressions. But the rules for adding, subtracting, multiplying, and dividing, however, are very much the same.

For addition and subtraction of rational expressions, the least common denominator, or LCD, of the expressions must be found. To find the LCD, we factor the denominators to find the unique factors which appear in all denominators and multiply these together to get the LCD. The equivalent numerators are derived by multiplying all the terms of the expressions with the factors (as a fraction equivalent to 1) not found in each corresponding denominator. All the numerators can then be added or subtracted since they are now similar, since their corresponding expressions all have the same denominator now. Simplifying the rational expression in the answer, when applicable, is also recommended.

When multiplying, we can just as easily multiply the numerators of the rational expressions and the denominators as well. Factoring also helps to eliminate common factors in the numerator and denominator so that the answers we initially get will already be the final answer without the need to simplify.

Division, being the inverse of multiplication, is done by flipping the numerator and denominator of the second expression. The expressions are then solved like a regular multiplication operation.

Rational expressions may look a bit daunting to solve, but operations on rational expressions are really quite easy when you know all the techniques.

Rewrite Rational Expressions.

CCSS.MATH.CONTENT.HSA.APR.D.7

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Exercises in this Practice Problem
Explain how to add or subtract rational expressions.
Multiply and divide the following rational expressions.
Find the expressions that can be simplified.
Determine the following expression.
Explain the meaning of LCD.
Calculate the given expressions.