Here are the essential concepts you must grasp in order to answer the question correctly.
Rational Expressions
Rational expressions are fractions where the numerator and the denominator are polynomials. Understanding how to manipulate these expressions is crucial for performing operations like addition and subtraction. In this case, the expressions 3x/(x−3) and (x+4)/(x+2) are rational expressions that need to be combined.
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Common Denominator
To add or subtract rational expressions, it is essential to find a common denominator. The common denominator is the least common multiple (LCM) of the individual denominators. For the given expressions, the common denominator would be the product of (x−3) and (x+2), allowing for the expressions to be combined correctly.
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Simplifying Expressions
After performing the addition or subtraction of rational expressions, the result often needs to be simplified. This involves factoring the numerator and denominator, canceling any common factors, and rewriting the expression in its simplest form. Simplifying helps in understanding the behavior of the expression and makes it easier to analyze.
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