Simplifying Rational Expressions

Simplifying Rational Expressions

How do I simplify (or reduce) rational expressions?

​What is a rational expression?

​A rational expression is the quotient of two polynomials.

Steps to simplify rational expressions:

Step 1: Factor the numerator completely (top number)

Step 2: Factor the denominator completely (bottom number)

Step 3: Cross out (cancel) common factors.

Some text here about the topic of discussion

How do we solve this problem?​

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​Correct Answer:

1. ​Combine Like Terms

   This Step is not necessary for this problem.

2. Factor polynomials

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3. Cancel out Common Factors

   We can cancel out the twos and the y's leaving us with the answer.​

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How do we solve this problem?​

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​Correct Answer:

1. ​Combine Like Terms

   Not necessary for this problem

2. Factor out polynomials​

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3. Cancel Out Common Factors​

   We can cancel ou​t (x-2), you will then have the correct answer

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How do we solve this problem?​

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​Correct Answer:

1. ​Combine Like Terms

   This is not necessary for this problem

2. Factor Polynomials​

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3. Cancel out Common Factors​

We can cancel out (n+5), giving us the correct answer.​

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Reviewing Simplifying Rational Expressions by Factoring

First, we will review how to simplify rational expressions by factoring, then you will be assessed on this material!

WATCH THIS!

Multiple Choice

What are the excluded values for

$$\frac{\left(x+3\right)}{\left(x+2\right)\left(x+1\right)}$$  

• $$x\ne2,\ x\ne1$$  

• $$x\ \ne\ -2,\ x\ \ne\ -1$$  

• $$x\ne-2,\ x\ne-1,\ x\ne-3$$  

• $$x\ne2,\ x\ne1,\ x\ne3$$  

Multiple Choice

What expression is equivalent to  $$\frac{\left(x-5\right)}{\left(x-5\right)\left(x-4\right)}$$  

• $$\frac{1}{x-4}$$

• $$x-4$$

• $$\frac{1}{-9x-4}$$

• $$-9x-4$$

Multiple Choice

What is the simplest form of $$\frac{x^2+5x-36}{x^2-16}$$  

• $$\frac{x+9}{x+4}$$  

• $$\frac{9}{4}$$  

• $$\frac{x+9}{x-4}$$  

• $$-\frac{9}{4}$$  

Multiple Choice

Which expression is equivalent to $$\frac{12x^4\left(x-3\right)\left(x+5\right)}{30x\left(x+3\right)\left(x+5\right)}$$  

• $$-\frac{2x^3}{5}$$  

• $$-\frac{x^3}{18}$$  

• $$\frac{x^3\left(x-3\right)}{18\left(x+3\right)}$$  

• $$\frac{2x^3\left(x-3\right)}{5\left(x+3\right)}$$  

Multiple Choice

Simplify the Expression

Multiple Choice

Simplify the Expression

Multiple Choice

Simplify

$$\frac{\left(2x-2x^2\right)}{\left(x-1\right)}$$  

• $$-2x$$  
  

• $$\frac{-1}{2x}$$  

• $$2x$$  
  

• $$\frac{1}{2x}$$  
  

Multiple Choice

Simplify

• A.(x+7)/(x+4)

• B.3/4

• C.(x+3)/(x+4)

• D.(x+3)/(x-4)