1. Examples for Multiplying And Dividing Rational Expressions

2. Monomials (Multiply Across Method)
The first method that can be used is to multiply across and then simplify.
Now that you have them multiplied together, simplify.
The two 12’s cancel out, because 12/12 is one. The x4 and x6 leave a x2 on the bottom. The y3 and y4 leave a y on the bottom of the equation . Therefore, the final answer is:

3. Monomials (Cross-Cancel Method)
With cross-cancelling, you can cancel out common factors in the numerator with the denominator. 2
In this first cross-cancel, both 4 and 2 can be divided by 2, therefore 4 becomes 2, and 2 becomes 1. 1 1
In this step, the 3 and the 6 can be divided since 3 goes into both 3 and 6 evenly. 3/3 is 1, and 3/6 is 2. 2 1
In this step, both of the 2x4s cancel out, and 2x4/2x4
Is 1, therefore they both become 1 1
Note: do not copy the rational down each time you cross-cancel, it is easier to do this all at once, it is done this way solely for example purposes.

4. Monomials (Cross Cancel Method)1
In this step both y4 and y3 can be divided by y3. So, y3/ y3 is 1, and y4 divided by y3 is y. y
Once you have simplified until you can’t simplify anymore, then just multiply across to get the answer. Notice, that this has the same final answer as using the other method.

5. Polynomials – Multiplying Across
First, factor. X^2-16 can be factored into (x+4)(x-4). 3x+12 can also be factored. Take out the 3, making it 3(x+4).
After factoring, multiply across. (x+4)(x+4) is the numerator and 3(x+4)(x+4)(x-4) is the denominator.
Then, cancel. The two (x+4) from the numerator cancel out with the two (x+4) from the denominator.
That is your final answer. The 1 takes the place of the (x+4) since there is nothing else on the top. You do not have to multiply back out.

6. Polynomials – Cross Cancel
The first step is to factor. The x^2-16 can factor will factor into (x+4)(x-4). The 3x+12 will factor into 3(x+4).
The next step is to cross out common factors in the numerator and denominator. In this problem, the two (x+4) cancel out.
The final step is to multiply the remaining factors across, getting a final answer of:
Notice that both methods result in the same answer.