Simplifying Rational Expressions

Rational Expressions a rational number can be expressed as a quotient of two integers. A rational expression can be expressed as a quotient of two polynomials.

Key concepts we need to know Anything divided by itself is 1 Zero product property if (a)(b)=0 then a=0; b=0; or a and b=0 You can’t divide by 0!!!!

Remember, denominators can not = 0. Now,lets go through the steps to simplify a rational expression.

Step 1: Factor the numerator and the denominator completely looking for common factors. Next

What value of x would make the denominator 0? The expression is undefined when the values make the denominator equal to 0 so, we state restrictions to the domain. x= -1,1

How do I find the values that make an expression undefined? Completely factor the original denominator.

Factor the denominator The expression is undefined when: a= 0, 2, and -2 and b= 0.

What is the common factor? Step 2: Divide the numerator and denominator by the common factor.

Step 3: Multiply to get your answer. 1 1 Step 3: Multiply to get your answer.

Lets go through another example. Factor out the GCF Next

State Restrictions What values of x will make the denominator =0?

1 1

Now try to do some on your own. Don’t forget to state the values that make each expression undefined?

Remember how to multiply fractions: First you multiply the numerators then multiply the denominators.

The same method can be used to multiply rational expressions. 1

Step #1: Factor the numerator and the denominator. Let’s do another one. Step #1: Factor the numerator and the denominator. Next

Step #2: Divide the numerator and denominator by the common factors. 1

Step #3: Multiply the numerator and the denominator. Remember how to divide fractions?

Multiply by the reciprocal of the divisor. 1 5 4

Dividing rational expressions uses the same procedure. Ex: Simplify

1 Next

Now you try to simplify the expression:

Now try these on your own.

Here are the answers: