QQuestionAdvanced Placement
QuestionAdvanced Placement
Explain the steps involved in adding two rational expressions.
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Answer
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Step 1:I'll solve this problem by explaining how to add rational expressions step by step:
Step 2:: Identify the Rational Expressions
A rational expression is a fraction where both the numerator and denominator are polynomials. To add rational expressions, they must have a common denominator.
Step 3:: Find the Least Common Denominator (LCD)
- The LCD is the least common multiple (LCM) of the denominators - This allows us to create equivalent fractions with the same denominator
Step 4:: Convert Each Fraction to an Equivalent Fraction with the LCD
Let's add $$\frac{2x}{x+1}$$ and $$\frac{3}{x+1}
- Multiply each fraction's numerator and denominator by the appropriate factor to reach the LCD - This preserves the original value of the fraction Example:
Step 5:: Combine the Numerators
- Since the denominators are already the same ($$x+1$$), simply add the numerators
\frac{2x}{x+ 1} + \frac{3}{x+ 1} = \frac{2x + 3}{x+ 1}
Step 6:: Simplify the Result (if possible)
- In this case, the fraction $$\frac{2x + 3}{x+1}$$ cannot be simplified further
- Check if the numerator can be factored or reduced
Final Answer
Key Insights: - Always find a common denominator first - Add only the numerators when denominators are the same - Simplify the result if possible
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