Published On:Thursday, 8 December 2011
Posted by Muhammad Atif Saeed
What Are Algebraic Fractions?
What Are Algebraic Fractions?
Algebraic fractions are fractions using a variable in the numerator or denominator, such as
. Because division by 0 is impossible, variables in the denominator have certain restrictions. The denominator can never equal 0. Therefore, in the fractions 
Operations with Algebraic Fractions
Many techniques will simplify your work as you perform operations with algebraic fractions. As you review the examples, note the steps involved in each operation and any methods that will save you time.Reducing algebraic fractions
To reduce an algebraic fraction to lowest terms, first factor the numerator and the denominator; then reduce, (or divide out) common factors.Example 1
Reduce.
Multiplying algebraic fractions
To multiply algebraic fractions, first factor the numerators and denominators that are polynomials; then, reduce where possible. Multiply the remaining numerators together and denominators together. (If you've reduced properly, your answer will be in reduced form.)Example 2
Multiply.
Dividing algebraic fractions
To divide algebraic fractions, invert the second fraction and multiply. Remember, you can reduce only after you invert.Example 3
Divide.
Adding or subtracting algebraic fractions
To add or subtract algebraic fractions having a common denominator, simply keep the denominator and combine (add or subtract) the numerators. Reduce if possible.Example 4
Perform the indicated operation.
Example 5
Perform the indicated operation.
Example 6
Perform the indicated operation.
Example 7
Perform the indicated operation.
Example 8
Perform the indicated operation.
