Questions and Answers
What is the simplified form of $\frac{10x}{x-2}$?
What is the simplified form of $\frac{6}{x-4}$?
What is the simplified form of $x + 7$?
What is the simplified form of $\frac{5(x+7)}{x+10}$?
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What is the simplified form of $\frac{8x}{x+4}$?
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What is the simplified form of $\frac{(x-10)}{(x-8)}$?
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What is the simplified form of $\frac{(x+7)}{2x}$?
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What is the simplified form of $\frac{4x^2}{(x+10)}$?
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What is the simplified form of $\frac{(x+6)}{(x+9)}$?
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What is the simplified form of $2(x-8)$?
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What is the simplified form of $\frac{6}{(x-6)}$?
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What is the simplified form of $\frac{1}{(m-3)}$?
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What is the simplified form of $n+5$?
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What is the simplified form of $\frac{7(x-1)}{(5x-8)}$?
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What is the simplified form of $\frac{1}{(p+2)}$?
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What is the simplified form of $\frac{3}{5(a-1)}$?
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What is the simplified form of $\frac{2}{3}$?
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What is the simplified form of $\frac{(p-5)}{(p-1)}$?
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What is the simplified form of $\frac{(x-2)}{(x+5)}$?
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What is the simplified form of $\frac{(a+1)}{(a+5)}$?
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What is the simplified form of $\frac{(x+3)}{(x-1)}$?
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What is the simplified form of $2b$?
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What is the simplified form of $\frac{-3}{(n+9)}$?
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What is the simplified form of $\frac{-7}{(b+10)}$?
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What is the simplified form of $\frac{(p-7)}{9(p-4)}$?
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What is the simplified form of $\frac{2x}{3}$?
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What is the simplified form of $-x+4$?
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What is the simplified form of $\frac{10}{(v+10)}$?
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What is the simplified form of $\frac{3}{(8n^2)}$?
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What is the simplified form of $\frac{(x+7)}{7}$?
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What is the simplified form of $\frac{5}{4a(a-1)}$?
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What is the simplified form of $\frac{3b}{(b+8)}$?
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What is the simplified form of $\frac{(p+7)}{7(p-10)}$?
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What is the simplified form of $\frac{7}{(6x)}$?
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What is the simplified form of $\frac{(p-3)}{(p-9)}$?
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What is the simplified form of $10$?
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What is the simplified form of $\frac{4x}{7}$?
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What is the simplified form of $\frac{4}{7}$?
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What is the simplified form of $2$?
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What is the simplified form of $\frac{1}{2}$?
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What is the simplified form of $\frac{x}{3(x+1)}$?
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What is the simplified form of $\frac{3x}{(x+1)}$?
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What is the simplified form of $\frac{(x-4)}{(x-7)}$?
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What is the simplified form of $\frac{(x+7)(x-4)}{(x-7)}$?
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What is the simplified form of $\frac{1}{(x-3)}$?
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What is the simplified form of $\frac{(x+3)}{(x-3)}$?
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What is the simplified form of $\frac{2(x-1)}{(3x-10)}$?
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What is the simplified form of $\frac{(x-1)}{(3x-10)}$?
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Study Notes
Rational Expressions Simplification Overview
- Rational expressions involve ratios of polynomials, which can often be simplified.
- Simplifying these expressions typically involves factoring, canceling common terms, or reducing to lowest terms.
Common Forms and Strategies
- Linear expressions: For expressions like ( \frac{10x}{x-2} ) and ( \frac{6}{x-4} ), look for common factors to simplify.
- Constant numerators: Expressions such as ( \frac{4}{7} ) or ( 10 ) are already simplified.
- Binomial expressions: Simplifying ( \frac{x+7}{x-10} ) requires examining factors but can often be reduced to lowest terms.
Specific Examples
- Example with a linear factor: ( \frac{5(x+7)}{x+10} ) simplifies but retains complexity due to the unique denominators.
- Denominators with linear terms: ( \frac{2(x-8)}{1} ) simplifies directly to ( 2(x-8) ).
- Complex fractions: Reducing fractions like ( \frac{(x+7)(x-4)}{x-7} ) often requires identifying common terms in the numerator and denominator.
Lowest Terms Importance
- Expressions such as ( \frac{1}{m-3} ) or ( \frac{7(x-1)}{5x-8} ) must be simplified to their lowest forms to ensure clarity and accuracy in mathematical communication.
- Expressions that are linear or constant often stabilize quickly, such as ( 2 ), ( \frac{1}{2} ), or ( \frac{3}{5(a-1)} ).
Simplification Techniques
- Factoring: Always look to factor where possible to simplify rational expressions effectively.
- Canceling: If a term is present in both the numerator and the denominator, it can often be canceled for simplification.
- Combining fractions: When dealing with complex rational expressions, combining them can help to reveal simplification opportunities.
Key Takeaways
- Simplifying rational expressions is a fundamental algebraic skill.
- Recognizing when terms can be canceled or factored out is crucial for effective simplification.
- Practicing with various forms of rational expressions enhances understanding and proficiency.
Studying That Suits You
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Description
Test your understanding of simplifying and manipulating rational expressions with these flashcards. Each card presents a rational expression that needs to be simplified. Perfect for Algebra 2 students looking to strengthen their skills in this topic!