Rational Expressions and Their Operations

This video tutorial covers rational expressions, focusing on simplifying, multiplying, dividing, and adding them. It begins with factoring techniques to simplify expressions, then moves on to multiplying expressions by factoring and canceling terms. The division of rational expressions is explained using the 'keep, change, flip' method. Finally, the video demonstrates how to add rational expressions by finding common denominators. Each section provides step-by-step instructions to help learners understand and solve problems involving rational expressions.

What is the first step in simplifying a rational expression?

• Add the numerators

• Factor the expression completely

• Multiply the denominators

• Subtract the numerators

Tags

CCSS.HSA.APR.C.4

When simplifying x^2 - 25, what form does it take after factoring?

• (x + 5)(x - 5)

• (x + 25)(x - 25)

• (x + 10)(x - 10)

• (x + 1)(x - 1)

Tags

CCSS.HSA.APR.D.7

What is the result of multiplying two rational expressions after factoring and canceling common terms?

• A single fraction with a common denominator

• A simplified expression with no common factors

• A product of the original numerators

• A sum of the original denominators

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CCSS.7.EE.A.1

What is the greatest common factor (GCF) of 4x - 12?

• 2

• 3

• 6

• 4

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CCSS.HSA.APR.D.6

What method is used to divide two rational expressions?

• Add and subtract

• Keep, change, flip

• Multiply and divide

• Factor and cancel

Tags

CCSS.HSA.APR.D.6

How do you rewrite a division problem into a multiplication problem when dividing rational expressions?

• Subtract the denominators and add the numerators

• Keep the first fraction, change the sign, flip the second fraction

• Flip both fractions and multiply

• Add the numerators and multiply the denominators

Tags

CCSS.HSA.APR.D.7

What is the first step in adding two rational expressions?

• Find a common denominator

• Subtract the denominators

• Divide the numerators

• Multiply the numerators

Tags

CCSS.HSA.APR.D.7

When adding rational expressions, what do you do after finding a common denominator?

• Multiply the numerators

• Add the numerators

• Divide the numerators

• Subtract the numerators

Tags

CCSS.7.EE.A.1

What is the result of combining like terms in the expression 2x^2 - 4x + 5x + 15?

• 2x^2 + x + 15

• 2x^2 - x + 15

• 2x^2 + 5x + 15

• 2x^2 + 9x + 15

Why can't the trinomial 2x^2 + x + 15 be factored further?

• It has no real roots

• The factors do not add up to the middle coefficient

• It is already in its simplest form

• The leading coefficient is not 1