Algebra Tutorials! Home Solving Quadratic Equations by Completing the Square Graphing Logarithmic Functions Division Property of Exponents Adding and Subtracting Rational Expressions With Like Denominators Rationalizing the Denominator Multiplying Special Polynomials Functions Solving Linear Systems of Equations by Elimination Solving Systems of Equation by Substitution and Elimination Polynomial Equations Solving Linear Systems of Equations by Graphing Quadratic Functions Solving Proportions Parallel and Perpendicular Lines Simplifying Square Roots Simplifying Fractions Adding and Subtracting Fractions Adding and Subtracting Fractions Solving Linear Equations Inequalities in one Variable Recognizing Polynomial Equations from their Graphs Scientific Notation Factoring a Sum or Difference of Two Cubes Solving Nonlinear Equations by Substitution Solving Systems of Linear Inequalities Arithmetics with Decimals Finding the Equation of an Inverse Function Plotting Points in the Coordinate Plane The Product of the Roots of a Quadratic Powers Solving Quadratic Equations by Completing the Square
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# Adding and Subtracting Rational Expressions With Like Denominators

After studying this lesson, you will be able to:

Add and subtract rational expressions with like denominators.

• Remember that when we add or subtract fractions, we must have a common denominator before we can add. The same is true for adding and subtracting rational expressions.
• Once we have a common denominator, we keep the denominator and we add the numerators. Collect like terms in the numerator.
• Next, simplify if possible by factoring, canceling, and/or reducing.

Example 1 We have a common denominator so we can add the numerators. This will not reduce so this is the answer.

Example 2 This is a subtraction problem, so we have to "add the opposite" before we do anything else. This means we will take the opposite of everything in the numerator that follows the subtraction sign. Now we are adding and we have a common denominator so we keep the denominator and add the numerators. This will not reduce so this is the answer

Example 3 This is a subtraction problem, so we have to "add the opposite" before we do anything else. This means we will take the opposite of everything in the numerator that follows the subtraction sign. Now we are adding and we have a common denominator so we keep the denominator and add the numerators. This will reduce - the numerator will factor. Cancel out the binomials 2 This is the final answer

Example 4 This is a subtraction problem, so we have to "add the opposite" before we do anything else. This means we will take the opposite of everything in the numerator that follows the subtraction sign. Now we are adding and we need a common denominator. Factor out -1 from the 2 - x Move the -1 to the top and we will have a common denominator. Distribute the -1 Add the numerators