Simplifying Algebraic Complex Fractions: Methods and Examples

What is the first step in Method One for simplifying complex fractions?

• Multiply the numerator and denominator by the least common denominator

• Add the fractions in the numerator and denominator

• Multiply the numerator by the reciprocal of the denominator

• Simplify the numerator and denominator to single fractions

In Method One, what do you do after simplifying the numerator and denominator to single fractions?

• Add the fractions in the numerator and denominator

• Divide the numerator by the denominator

• Multiply the numerator by the reciprocal of the denominator

• Multiply the numerator and denominator by the least common denominator

What is the key step in Method Two for simplifying complex fractions?

• Simplify the numerator and denominator to single fractions

• Multiply the numerator and denominator by the least common denominator

• Add the fractions in the numerator and denominator

• Multiply the numerator by the reciprocal of the denominator

Why is Method Two especially useful?

• It is easier to understand

• It is faster than Method One

• It requires fewer steps

• It works well when there are plus signs in the numerator or denominator

What happens to the fractions in the numerator and denominator when using Method Two?

• They are added together

• They are divided

• They are multiplied by the reciprocal

• They are eliminated

In Method One, what do you do after getting a common denominator in the numerator and denominator?

• Multiply the numerator by the reciprocal of the denominator

• Simplify the fractions

• Add the fractions in the numerator and denominator

• Multiply the numerator and denominator by the least common denominator

What is the least common denominator (LCD) in the example problem with 3 over x plus 2, plus 5 over x minus 2?

• x squared minus 4

• x minus 2

• x squared

• x plus 2

What is the final simplified form of the complex fraction 3 over x plus 2, plus 5 over x minus 2, all over 4 over x squared minus 4?

• 5x minus 2

• 4x plus 1

• 2x plus 1

• 3x minus 2

When is Method Two usually easier to use?

• When the fractions are already simplified

• When the least common denominator is easy to find

• When there are addition problems with fractions in the numerator or denominator

• When there is a single fraction in the numerator or denominator

What is the final answer for the simple arithmetic problem with a single fraction in the numerator and denominator?

• 3 over 2

• 6 over 5

• 5 over 6

• 2 over 3