Simplifying Algebraic Fractions

This video tutorial covers the simplification of algebraic fractions through six examples. It introduces the golden rule of multiplying or dividing the numerator and denominator by the same number and explains factorization techniques. Each example demonstrates different methods, including the use of common factors, difference of squares, and quadratic factorization. The video concludes by addressing common mistakes in simplification.

What is the main focus of this video tutorial?

• Understanding complex numbers

• Graphing linear equations

• Simplifying algebraic fractions

• Solving quadratic equations

What is the golden rule for simplifying fractions?

• Only multiply the numerator by a constant

• Subtract the same number from both numerator and denominator

• Multiply or divide both numerator and denominator by the same number

• Add the same number to both numerator and denominator

In the example of simplifying 4/8, what operation is performed?

• Adding 4 to both numerator and denominator

• Dividing both numerator and denominator by 4

• Subtracting 2 from both numerator and denominator

• Multiplying both numerator and denominator by 2

What is the result of simplifying 15x^2y/10xy^2 using the golden rule?

• 3x/2y

• 15x/10y

• 3xy/2

• 3x^2/2y^2

How do you factorize the expression 4c + 6?

• By dividing by 4

• By factoring out a 2

• By adding 2 to each term

• By multiplying by 3

What is the simplified form of (5y + 10)/(3y + 6)?

• 5/3y

• 5y + 10/3y + 6

• 5y/3y

• 5/3

In question D, what is the common factor in the numerator a^3b^2 + a^2b?

• a^2b

• a^3

• a^2

• b^2

What technique is used to factorize the denominator x^2 - 4 in question E?

• Completing the square

• Quadratic formula

• Synthetic division

• Difference of two squares

In question F, what are the factors of the expression x^2 + 5x + 6?

• (x + 2)(x + 3)

• (x + 2)(x - 3)

• (x + 1)(x + 6)

• (x + 3)(x + 2)

Why is it incorrect to cancel out terms that are added in a fraction?

• Because it simplifies the fraction correctly

• Because it changes the fraction to multiplication

• Because it violates the golden rule

• Because it only works for subtraction