Easy Medium Hard Simplify Complex Fractions

Brian McLogan2 minutes read

Complex fractions involve finding the least common multiple of denominators, then multiplying each expression to simplify the fraction by eliminating fractions. Factors like trinomials and binomials can be simplified in a medium complexity example by identifying the least common multiple and rewriting negative powers as reciprocals to avoid fractions in the denominator.

Insights

  • Complex fractions involve fractions in both the numerator and denominator, requiring the elimination of fractions by finding the least common multiple of the denominators.
  • When simplifying complex fractions, factor trinomials and binomials, identify the least common multiple of the denominators, rewrite negative powers as reciprocals, and apply the distributive property to combine like terms for a comprehensive simplification process.

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Recent questions

  • How do you simplify complex fractions?

    By finding the least common multiple of denominators.

  • What is the key step in simplifying complex fractions?

    Identifying the least common multiple of denominators.

  • How to handle fractions with varying degrees of variables?

    Ensure all expressions can divide into the least common multiple.

  • What should be done with negative powers in complex fractions?

    Rewrite them as reciprocals to avoid fractions in the denominator.

  • How to eliminate additional fractions in the denominator of complex fractions?

    Use equivalent fractions by multiplying with the appropriate term.

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Summary

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Simplify Complex Fractions with Multiple Denominators

  • Complex fractions involve fractions in both the numerator and denominator, requiring the elimination of fractions by finding the least common multiple of the denominators.
  • To simplify, multiply the least common multiple by each expression within the complex fraction separated by addition or subtraction.
  • In a medium complexity example with different denominators, factor trinomials and binomials to simplify the expression.
  • Identify the least common multiple of the denominators to ensure all expressions can divide into it.
  • Multiply each expression by the least common multiple to simplify the complex fraction.
  • When faced with negative powers, rewrite them as reciprocals to avoid fractions in the denominator.
  • Use equivalent fractions to eliminate additional fractions in the denominator by multiplying by the appropriate term.
  • For complex fractions with varying degrees of variables, ensure all expressions can divide into the least common multiple.
  • Apply distributive property and combine like terms to simplify the complex fraction, considering further factoring for additional simplification if required.
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