Simplifying Rational Expressions and Fractions

This video tutorial explains how to simplify algebraic fractions by factorizing numerators and denominators and canceling common terms. It covers several examples, including basic fractions, quadratic expressions, and complex fractions with fractions inside. The video emphasizes the importance of identifying common factors and using them to simplify expressions effectively.

What is the first step in simplifying the numerical fraction 10/15?

• Subtract 5 from both the numerator and denominator

• Add 5 to both the numerator and denominator

• Divide both the numerator and denominator by 5

• Multiply both the numerator and denominator by 5

In the fraction x + 3 over 2x + 6, what can be factorized in the denominator?

• x

• 3

• 2

• 2x + 6

What is the simplified form of the fraction x + 3 over 2x + 6?

• x + 3

• x/2

• 1/2

• 2/3

When simplifying 4x^2 + 2xy over 6x + 3y, what common factor can be taken out from the numerator?

• 4x

• 2x

• x

• 2

What is the simplified form of 4x^2 + 2xy over 6x + 3y?

• 2/3x

• 2x/3

• 2x + 3y

• 2x + y

What are the factors of the quadratic x^2 + 5x + 4?

• x + 3 and x + 1

• x + 4 and x + 4

• x + 2 and x + 2

• x + 1 and x + 4

What is the simplified form of x^2 + 5x + 4 over x^2 + 8x + 16?

• x + 4 over x + 4

• x + 1 over x + 1

• x + 4 over x + 1

• x + 1 over x + 4

What is the simplified form of x^2 - 25 over 10x + 50?

• x - 5 over 5

• x + 5 over 10

• x - 5 over 10

• x + 5 over 5

What common multiple is chosen to simplify the fraction 1/2x + 1 over 1/3x + 2/3?

• 2

• 3

• 5

• 6

What is the simplified form of 1/2x + 1 over 1/3x + 2/3 after multiplying by the common multiple?

• 3x + 4 over 2x + 4

• 3x + 6 over 2x + 4

• 3x + 4 over 2x + 6

• 3x + 6 over 2x + 6