Algebra II 5.08: Complex Fractions Quiz

Questions and Answers

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 $\frac{c^2 - 4c + 4}{12c^3 + 30c^2} \div \frac{c^2 - 4}{6c^4 + 15c^3}$?

$\frac{c(c - 2)}{2(c + 2)}$ (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 $\frac{3x}{x + 3} + \frac{x}{x + 2}$?

$\frac{3x^2 + 10x}{(x + 3)(x + 2)}$

$\frac{4x^2 + 9x}{(x + 3)(x + 2)}$ (correct)

$\frac{3x^2 + 9x}{(x + 3)(x + 2)}$

$\frac{5x^2 + 7x}{(x + 3)(x + 2)}$

Which expression is equal to $\frac{8m^2 + 16m}{m - 3} \times \frac{m^2 - m - 6}{4m^3 + 8m^2}$?

$\frac{2(m + 2)}{m}$ Signup and view all the answers

Enter the simplified form of the complex fraction: $(\frac{2}{x - 3}) - (\frac{-3}{x}) / \frac{3}{3 - x}$.

$\frac{-x + 9}{3x}$ Signup and view all the answers

Which expression is equal to $\frac{2x}{x - 2} - \frac{x + 3}{x + 5}$?

$\frac{x^2 + 11x + 6}{(x - 2)(x + 5)}$ Signup and view all the answers

Which expression is equal to $\frac{c^2 - 4}{6c^4 + 15c^3} \div \frac{c^2 - 4c + 4}{12c^3 + 30c^2}$?

$\frac{2(c + 2)}{c(c - 2)}$ Signup and view all the answers

Which expression is equal to $\frac{3x}{x + 3} + \frac{x + 2}{x}$?

$\frac{4x^2 + 5x + 6}{x(x + 3)}$ Signup and view all the answers

Which expression is equal to $\frac{4p^2 + 32p}{p - 2} \times \frac{p^2 + p - 6}{2p^3 + 16p^2}$?

$\frac{2(p + 3)}{p}$ Signup and view all the answers

Enter the simplified form of the complex fraction: $(\frac{2}{x - 1}) + (\frac{1}{x}) / \frac{8}{x}$.

$\frac{3x - 1}{8(x - 1)}$ Signup and view all the answers

Which expression is equal to $\frac{(6a^2 - 30a)}{a - 2} \times \frac{a^2 + 2a - 8}{2a^3 - 10a^2}$?

$\frac{3a + 12}{a}$ Signup and view all the answers

Enter the simplified form of the complex fraction: $(\frac{3}{x}) + (\frac{1}{4}) / (1 + (\frac{3}{x}))$.

$\frac{12 + x}{4x + 12}$ Signup and view all the answers

Which expression is equal to $\frac{2x}{x - 2} - \frac{x + 5}{x + 3}$?

$\frac{x^2 + 3x + 10}{(x - 2)(x + 3)}$ Signup and view all the answers

Which expression is equal to $\frac{c^2 - 4}{6c^4 + 15c^3} \div \frac{c^2 + 4c + 4}{12c^3 + 30c^2}$?

$\frac{2(c - 2)}{c(c + 2)}$ Signup and view all the answers

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} )
Simplified*: ( \frac{c(c - 2)}{2(c + 2)} )
Expression: ( \frac{3x}{x+3} + \frac{x}{x+2} )
Simplified*: ( \frac{4x^2 + 9x}{(x+3)(x+2)} )
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

Expression: ( \frac{\frac{2}{x-3} - \left(-\frac{3}{x}\right)}{\frac{3}{3-x}} )
Simplified*: ( \frac{-x + 9}{3x} )
Expression: ( \frac{2x}{x-2} - \frac{x+3}{x+5} )
Simplified*: ( \frac{x^2 + 11x + 6}{(x-2)(x+3)} )
Expression: ( \frac{c^2 - 4}{6c^4 + 15c^3} ÷ \frac{c^2 - 4c + 4}{12c^3 + 30c^2} )
Simplified*: ( \frac{2(c + 2)}{c(c - 2)} )
Expression: ( \frac{3x}{x+3} + \frac{x+2}{x} )
Simplified*: ( \frac{4x^2 + 5x + 6}{x(x+3)} )

More Complex Expressions

Expression: ( \frac{4p^2 + 32p}{p - 2} \times \frac{p^2 + p - 6}{2p^3 + 16p^2} )
Simplified*: ( \frac{2(p + 3)}{p} )
Expression: ( \frac{\frac{2}{x - 1} + \frac{1}{x}}{\frac{8}{x}} )
Simplified*: ( \frac{3x - 1}{8(x - 1)} )

Final Complex Fractions

Expression: ( \frac{3/x + 1/4}{1 + 3/x} )
Simplified*: ( \frac{12 + x}{4x + 12} )
Expression: ( \frac{2x}{x - 2} - \frac{x + 5}{x + 3} )
Simplified*: ( \frac{x^2 + 3x + 10}{(x - 2)(x + 3)} )
Expression: ( \frac{c^2 - 4}{6c^4 + 15c^3} ÷ \frac{c^2 + 4c + 4}{12c^3 + 30c^2} )
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.

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.