Rational Expressions and Fractions

The video tutorial explains how to add and subtract rational expressions with unlike denominators. It begins with an introduction to the concept and outlines the steps to find the least common denominator (LCD) by factoring denominators. Two examples are provided: one for adding fractions and another for subtracting fractions. Each example demonstrates how to rewrite fractions with a common denominator, perform the arithmetic operation, and simplify the result.

What is the first step in adding or subtracting rational expressions with unlike denominators?

• Simplify the fractions

• Add the numerators

• Find a common denominator

• Multiply the numerators

In the first example, what is the least common denominator (LCD) for the fractions 5/6x and 7/9x?

• 18x

• 6x

• 9x

• 12x

How do you create equivalent fractions with the LCD in the first example?

• Add the numerators directly

• Multiply the numerator and denominator of each fraction by missing factors

• Multiply both denominators by 3

• Multiply both numerators by 2

What is the final sum of the fractions in the first example?

• 30/18x

• 29/18x

• 15/18x

• 14/18x

In the second example, what is the first step in factoring x^2 + x?

• Factor out the greatest common factor

• Divide by x

• Add x to both terms

• Multiply by x

What is the least common denominator (LCD) for the fractions 2/x^2 and 1/(x^2 + x) in the second example?

• x^3

• x(x + 1)

• x^2(x + 1)

• x^2

How do you rewrite the first fraction in the second example with the LCD?

• Multiply by x

• Add x to the numerator

• Divide by x

• Multiply by x + 1

What is the simplified difference of the fractions in the second example?

• x^2 + 2

• x + 1

• x + 2

• 2x + 1

Why is it important not to simplify the fractions before subtracting in the second example?

• It adds extra steps

• It loses the common denominator

• It changes the numerators

• It makes the fractions larger

What is the final form of the denominator in the second example after rewriting the fractions?

• x^2

• x^3

• x(x + 1)

• x^2(x + 1)