Podcast
Questions and Answers
Which expression is equal to $\frac{2x}{x+2} - \frac{x-3}{x+5}$?
Which expression is equal to $\frac{2x}{x+2} - \frac{x-3}{x+5}$?
- $\frac{x^2 + 11x + 6}{(x+2)(x+5)}$ (correct)
- $\frac{x^2 + 10x + 6}{(x+2)(x+5)}$
- $\frac{x^2 + 12x + 6}{(x+2)(x+5)}$
- $\frac{x^2 + 11x + 7}{(x+2)(x+5)}$
Which expression is equal to $\frac{c^2 - 4c + 4}{12c^3 + 30c^2} \div \frac{c^2 - 4}{6c^4 + 15c^3}$?
Which expression is equal to $\frac{c^2 - 4c + 4}{12c^3 + 30c^2} \div \frac{c^2 - 4}{6c^4 + 15c^3}$?
- $\frac{c(c - 2)}{2(c + 2)}$ (correct)
- $\frac{4(c - 2)}{c(c + 2)}$
- $\frac{c(c + 2)}{2(c - 2)}$
- $\frac{c(c + 4)}{2(c - 2)}$
Which expression is equal to $\frac{3x}{x + 3} + \frac{x}{x + 2}$?
Which expression is equal to $\frac{3x}{x + 3} + \frac{x}{x + 2}$?
- $\frac{3x^2 + 10x}{(x + 3)(x + 2)}$
- $\frac{4x^2 + 9x}{(x + 3)(x + 2)}$ (correct)
- $\frac{3x^2 + 9x}{(x + 3)(x + 2)}$
- $\frac{5x^2 + 7x}{(x + 3)(x + 2)}$
Which expression is equal to $\frac{8m^2 + 16m}{m - 3} \times \frac{m^2 - m - 6}{4m^3 + 8m^2}$?
Which expression is equal to $\frac{8m^2 + 16m}{m - 3} \times \frac{m^2 - m - 6}{4m^3 + 8m^2}$?
Enter the simplified form of the complex fraction: $(\frac{2}{x - 3}) - (\frac{-3}{x}) / \frac{3}{3 - x}$.
Enter the simplified form of the complex fraction: $(\frac{2}{x - 3}) - (\frac{-3}{x}) / \frac{3}{3 - x}$.
Which expression is equal to $\frac{2x}{x - 2} - \frac{x + 3}{x + 5}$?
Which expression is equal to $\frac{2x}{x - 2} - \frac{x + 3}{x + 5}$?
Which expression is equal to $\frac{c^2 - 4}{6c^4 + 15c^3} \div \frac{c^2 - 4c + 4}{12c^3 + 30c^2}$?
Which expression is equal to $\frac{c^2 - 4}{6c^4 + 15c^3} \div \frac{c^2 - 4c + 4}{12c^3 + 30c^2}$?
Which expression is equal to $\frac{3x}{x + 3} + \frac{x + 2}{x}$?
Which expression is equal to $\frac{3x}{x + 3} + \frac{x + 2}{x}$?
Which expression is equal to $\frac{4p^2 + 32p}{p - 2} \times \frac{p^2 + p - 6}{2p^3 + 16p^2}$?
Which expression is equal to $\frac{4p^2 + 32p}{p - 2} \times \frac{p^2 + p - 6}{2p^3 + 16p^2}$?
Enter the simplified form of the complex fraction: $(\frac{2}{x - 1}) + (\frac{1}{x}) / \frac{8}{x}$.
Enter the simplified form of the complex fraction: $(\frac{2}{x - 1}) + (\frac{1}{x}) / \frac{8}{x}$.
Which expression is equal to $\frac{(6a^2 - 30a)}{a - 2} \times \frac{a^2 + 2a - 8}{2a^3 - 10a^2}$?
Which expression is equal to $\frac{(6a^2 - 30a)}{a - 2} \times \frac{a^2 + 2a - 8}{2a^3 - 10a^2}$?
Enter the simplified form of the complex fraction: $(\frac{3}{x}) + (\frac{1}{4}) / (1 + (\frac{3}{x}))$.
Enter the simplified form of the complex fraction: $(\frac{3}{x}) + (\frac{1}{4}) / (1 + (\frac{3}{x}))$.
Which expression is equal to $\frac{2x}{x - 2} - \frac{x + 5}{x + 3}$?
Which expression is equal to $\frac{2x}{x - 2} - \frac{x + 5}{x + 3}$?
Which expression is equal to $\frac{c^2 - 4}{6c^4 + 15c^3} \div \frac{c^2 + 4c + 4}{12c^3 + 30c^2}$?
Which expression is equal to $\frac{c^2 - 4}{6c^4 + 15c^3} \div \frac{c^2 + 4c + 4}{12c^3 + 30c^2}$?
Study Notes
Complex Fractions Simplification
- Complex fractions involve ratios with fractions in the numerator, denominator, or both.
- Simplification can often be achieved through finding common denominators and combining the fractions.
Key Expressions and Simplifications
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Expression: ( \frac{2x}{x+2} - \frac{x-3}{x+5} )
-
Simplified*: ( \frac{x^2 + 11x + 6}{(x+2)(x+5)} )
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Expression: ( \frac{c^2 - 4c + 4}{12c^3 + 30c^2} ÷ \frac{c^2 - 4}{6c^4 + 15c^3} )
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Simplified*: ( \frac{c(c - 2)}{2(c + 2)} )
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Expression: ( \frac{3x}{x+3} + \frac{x}{x+2} )
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Simplified*: ( \frac{4x^2 + 9x}{(x+3)(x+2)} )
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Expression: ( \frac{8m^2 + 16m}{m - 3} \times \frac{m^2 - m - 6}{4m^3 + 8m^2} )
-
Simplified*: ( \frac{2(m + 2)}{m} )
Additional Complex Fractions
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Expression: ( \frac{\frac{2}{x-3} - \left(-\frac{3}{x}\right)}{\frac{3}{3-x}} )
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Simplified*: ( \frac{-x + 9}{3x} )
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Expression: ( \frac{2x}{x-2} - \frac{x+3}{x+5} )
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Simplified*: ( \frac{x^2 + 11x + 6}{(x-2)(x+3)} )
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Expression: ( \frac{c^2 - 4}{6c^4 + 15c^3} ÷ \frac{c^2 - 4c + 4}{12c^3 + 30c^2} )
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Simplified*: ( \frac{2(c + 2)}{c(c - 2)} )
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Expression: ( \frac{3x}{x+3} + \frac{x+2}{x} )
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Simplified*: ( \frac{4x^2 + 5x + 6}{x(x+3)} )
More Complex Expressions
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Expression: ( \frac{4p^2 + 32p}{p - 2} \times \frac{p^2 + p - 6}{2p^3 + 16p^2} )
-
Simplified*: ( \frac{2(p + 3)}{p} )
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Expression: ( \frac{\frac{2}{x - 1} + \frac{1}{x}}{\frac{8}{x}} )
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Simplified*: ( \frac{3x - 1}{8(x - 1)} )
Final Complex Fractions
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Expression: ( \frac{3/x + 1/4}{1 + 3/x} )
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Simplified*: ( \frac{12 + x}{4x + 12} )
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Expression: ( \frac{2x}{x - 2} - \frac{x + 5}{x + 3} )
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Simplified*: ( \frac{x^2 + 3x + 10}{(x - 2)(x + 3)} )
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Expression: ( \frac{c^2 - 4}{6c^4 + 15c^3} ÷ \frac{c^2 + 4c + 4}{12c^3 + 30c^2} )
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Simplified*: ( \frac{2(c - 2)}{c(c + 2)} )
Study Tips
- Look for common factors to simplify each fraction before performing operations.
- Always ensure no denominator equals zero to avoid undefined expressions.
Studying That Suits You
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Description
Test your knowledge on simplifying complex fractions with this quiz. Each question challenges you to find equivalent expressions and practice algebraic manipulation. Perfect for students in Algebra II looking to reinforce their understanding of complex fractions.
