Simplifying Algebraic Fractions: Key Concepts and Examples

This video tutorial covers the simplification of algebraic fractions, a crucial topic for GCSE and A-level students. It begins with an introduction to algebraic fractions and common mistakes students make. The video then demonstrates how to simplify fractions using numerical examples, highlighting the importance of identifying common factors. It addresses common errors in simplification and provides advanced techniques for handling complex fractions. The tutorial emphasizes the need for careful factorization and the correct application of simplification rules to avoid errors.

What is the simplified form of 10 divided by 2?

• 2

• 5

• 10

• 1

When simplifying 10/2, what common factor is used to divide both the numerator and the denominator?

• 1

• 2

• 10

• 5

What is the correct way to simplify 21 + 15 divided by 3?

• 21 + (15 / 3)

• 21 / 3 + 15 / 3

• (21 + 15) / 3

• (21 + 15) * 3

What is the simplified form of (21 + 15) / 3?

• 12

• 7

• 36

• 5

What should you do if there is a common factor in every term of the numerator and the denominator?

• Divide only the numerator by the common factor

• Divide only the denominator by the common factor

• Divide every term in both the numerator and the denominator by the common factor

• Do nothing

How do you simplify the fraction (ax + bx) / x?

• a + b

• a / x + b / x

• ax + bx

• a + b / x

What is the simplified form of (x^2 - x - 6) / (x^2 - 3x)?

• (x + 2) / x

• (x + 2) / (x - 3)

• (x - 3) / (x + 2)

• (x - 3) / x

What is the simplified form of (x^2 - 4) / (x^2 - 4)?

• 1

• 0

• x - 2

• x + 2

What is the simplified form of (x^2 - 10x + 25) / (x^2 - 5x)?

• (x + 5) / x

• (x - 5) / x

• (x + 5) / (x - 5)

• (x - 5) / (x + 5)

What is the simplified form of (x^3 - 4x) / (x^2 - 4)?

• x(x - 2)

• x(x + 2) / (x - 2)

• x(x - 2) / (x + 2)

• x(x + 2)