Adding & Subtracting Rational Expressions

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In this section, we review how to add and subtract rational expressions. To perform either operation, we must have a common denominator. For easier problems, a common denominator will already exist. When we encounter tougher problems, we will need to obtain a common denominator. The preferred method is to find the LCD (Least Common Denominator) by factoring each denominator. We can then transform each rational expression into an equivalent one, where the LCD is its denominator. When we have a common denominator, we perform the operations with the numerator only and place the result over the common denominator. This is true for both addition of rational expressions, along with subtraction of rational expressions. The final step is to factor the rational expression and see if we can cancel any common factors between the numerator and denominator. We always want to leave our rational expression in simplified form.
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