Multiply and Divide Rational Expressions

[AngelShare]

I thought I knew what I was doing (because I've done this before) but I can't see what's happening in this one example...I understood what was going on right up until the last step.

If you are dividing two rational expressions, flip the second expression and multiply the two rational expressions together.
Multiply the numerators and the denominators. Because you want to cancel out the common factors, it is best not to actually multiply the numbers but instead to just write them together.
Factor the numerator and denominator completely.
Cancel the common factors.
The final answer consists of the remaining factors.

Q. 18a^2 (a-1)/5 * 25/6a
A. 5a(a - 1)

 

[TD]

I either made a mistake understanding the problem, or one of the (Q or A) has to be wrong.

\frac{{18a^2 \left( {a - 1} \right)}}<br /> {5} \cdot \frac{{25}}<br /> {{6a}} = \frac{{3a \cdot 6a \cdot \left( {a - 1} \right) \cdot 5 \cdot 5}}<br /> {{5 \cdot 6a}}

Now, what would cancelling out common factors give?

 

[AngelShare]

Aha! I thought so because that makes no sense. I'll post where I think it went wrong to see if I'm right. ^_^

Lesson work:

Step 2- Cancel the common factors

2*3*3*a*a*(a - 1)/5 * 5*5/2*3*a (What's bolded is what is left behind after cancellation.)

Step 3- Write the final answer

5a(a - 1)

My work:

Step 3- Write the final answer

3a(a - 1) * 5

3a^2 - 3a * 5

15a^2 - 15a

Being that the 5 was a separate fraction before cancellation, I thought I had to distribute it instead of just multiply it by one so...^_^

 

[AngelShare]

Could someone please tell me if my answer is correct before I move on? ^_^

 

[HallsofIvy]

Yes, your answer is correct. It can be written either 15a²- 15a or 15a(a-1).