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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

 

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