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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 $\frac{c^2 - 4}{6c^4 + 15c^3} \div \frac{c^2 + 4c + 4}{12c^3 + 30c^2}$?
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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
-
Expression: ( \frac{2x}{x+2} - \frac{x-3}{x+5} )
-
Simplified*: ( \frac{x^2 + 11x + 6}{(x+2)(x+5)} )
-
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} )
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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.
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