When going about getting a Least Common Denominator (LCD) what should you do first?

factor every denominator that can be factored

How did the denominator of x 2 -64 factor?

By Difference of Squares: (x-8)(x+8)

By Difference of Squares: (x-8)

By Greatest Common Factor: x(x-8)

Why does the other denominator not factor? Select all that apply.

Because it does not have a GCF and since it is only two terms, the only other way it could factor is by Difference of Squares. Which it is not that either.

Once you have a common denominator, what do you do next in the problem?

Add the numerators only and then simplify.

Add the numerators and the denominators and then simplify.

How did each denominator factor?

One denominator factored by GCF and the other was Prime

One denominator factored by GCF and the other factored by Difference of Squares.

One denominator factored by GCF and the other factored by a trinomial strategy.

Why did she not need to multiply the second fraction?

She did, she had to multiply it by 2

When you are ready to subtract rational expressions, what do you need to be sure you remember to do? Select all that apply.

Distribute the subtraction sign to every term that comes after it

Once she combined like terms in the numerator. What did she do next?

She looked to see if it could be factored

She circled it as her final answer

After she factored the numerator, why was she then able to cancel out the x-5 in the numerator and the denominator? Select all that apply.

Because they were written as factors (meaning: they were shown multiplying with another value)

What is the first step in simplifying: $$\frac{4}{x+3}+\frac{8}{x+5}$$ ?

Change to: $$\frac{4\left(x+5\right)}{\left(x+3\right)\left(x+5\right)}+\frac{8\left(x+3\right)}{\left(x+3\right)\left(x+5\right)}$$

Change to: $$\frac{20}{x+15}+\frac{24}{x+15}$$

Change to: $$\frac{20x}{x^2+15}+\frac{24x}{x^2+15}$$

Change to: $$\frac{20}{\left(x+3\right)\left(x+5\right)}+\frac{24}{\left(x+3\right)\left(x+5\right)}$$

What is the first step you should take when multiplying or dividing rational expressions?

Factor every polynomial that is factorable in each fraction.

multiply the numerators together and multiply the denominators together.

Once you get everything factored what do you do next?

Cancel out common factors that are in the numerator and the denominator of the fractions.

Multiply the numerators and then multiply the denominators

What are you trying to figure out when the problem asks "state any excluded values for x?"

You are finding any values for x that would make the denominator equal zero.

You are finding any values for x that would make the numerator equal zero.

When finding excluded values for x, you are setting your denominator factors equal to zero and solving for each senario. Which factors do you use when doing this?

You use the factors from when you first factored each of the denominators.

You use the factors from your final solution.

If you are dividing rational expressions, what must you also do first along with factoring every polynomial that can factor? Select all that apply.

Multiply by the reciprocal of the second fraction

Change the division symbol to a multiplication and then "flip" the second fraction.

Multiply by the reciprocal of the first fraction

Change the division symbol to a multiplication and then "flip" both of the fractions.

What type of factoring strategies did the polynomials have?

Difference of squares or trinomials where $$a\ne1$$

Review Op’s Rational Express_Interactive Video

Interactive Video

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Mathematics

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8th - 12th Grade

•

Practice Problem

•

Medium

•

CCSS

HSA.APR.D.7, HSA.APR.D.6, HSF-IF.C.7D

Standards-aligned

Erin McCreery

Used 7+ times

FREE Resource

Standards-aligned

CCSS.HSA.APR.D.7

CCSS.HSA.APR.D.6

CCSS.HSF-IF.C.7D

CCSS.4.NF.B.3C

CCSS.5.NF.A.1

CCSS.4.NF.B.3D

CCSS.5.NF.A.2

33 questions

Show all answers

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Simplify the rational expression.
*Remember: first you want to factor each polynomial if possible.

( x + 5 )( x - 5 ) / ( x + 5 )( x - 2 )

( x - 5 ) / ( x - 2 )

( x + 5 ) / ( x - 2 )

Tags

CCSS.HSA.APR.D.6

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Tags

CCSS.HSA.APR.D.7

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Simplify.

Tags

CCSS.HSA.APR.D.7

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Simplify.

Tags

CCSS.HSA.APR.D.7

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Multiply

Tags

CCSS.HSA.APR.D.7

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

(x - 5)/ (x - 1)

(x + 1)/(x - 1)

1/(x - 1)

(x + 1)

Tags

CCSS.HSA.APR.D.6

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

What is a rational expression?

A fraction

A fraction that has variables in the denominator

A ratio

Tags

CCSS.HSA.APR.D.7

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Review Op’s Rational Express_Interactive Video

33 questions

Simplify the rational expression. *Remember: first you want to factor each polynomial if possible.

Simplify.

Simplify.

Multiply

What is a rational expression?

What is the first step you should take when multiplying or dividing rational expressions?

When going about getting a Least Common Denominator (LCD) what should you do first?

How did the denominator of x2-64 factor?

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Simplify the rational expression.
*Remember: first you want to factor each polynomial if possible.

How did the denominator of x²-64 factor?