multiplying rational expressions

[gurrry]

This question is absolutely killing me. I cant get the right answer no matter what I do.


a^2 - 1 15a - 6
2 - 5a multiplied by 2 - a



First, I break down the a^2 - 1 into (a+1)(a-1).

Then, I look at the rest and start hyperventilating over it. I dont know what to do with the rest. Do I need to change the 2 - a into -a + 2? Im just flabbergasted by this problem.

 

[tkhunny]

\(\displaystyle \frac{a^{2}-1}{2-5a}\cdot\frac{15a-6}{2-a}\)

What are you to do? Simplify? There may not be much to do.

Don't worry about things looking a little backwards. Get used to switching them around if you feel it is necessary.

2 - 5a = -5a + 2 = -(5a-2)

And this is even cooler.

(2-5a)*(2-a) = [-(5a-2)][-(a-2)] = (5a-2)(a-2)

That's about all we can do with the denominator.

\(\displaystyle \frac{a^{2}-1}{5a-2}\cdot\frac{15a-6}{a-2}\)

We can factor the top a bit. You have already (a+1)(a-1). Now notice a common factor in the right-hand one. 15a-6 = 3(5a-2) That's about it. Now we have:

\(\displaystyle \frac{(a+1)(a-1)}{5a-2}\cdot\frac{3(5a-2)}{a-2}\)

Ah, now there is some simplifying to do. Do you see it?

 

[gurrry]

Wow...


Thank you so much. My problem was that I didnt notice the common factor in 15a - 6. I guess the way the problem looked just threw me off.

 

[mmm4444bot]

a^2 - 1 15a - 6
2 - 5a multiplied by 2 - a

We cannot draw fractions at this web site.

Please use grouping symbols, instead:

(a^2 - 1)/(2 - 5a) * (15a - 6)/(2 - a)