SOLUTION: I am having some problems with some multiplying and dividing of polynomial fractions, and with a addition and subtraction problem. Can you help? 3y-15 over 14 / y-5 over 4y -

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I am having some problems with some multiplying and dividing of polynomial fractions, and with a addition and subtraction problem. Can you help? 3y-15 over 14 / y-5 over 4y -       Log On


   

Question 227879: I am having some problems with some multiplying and dividing of polynomial fractions, and with a addition and subtraction problem. Can you help?
3y-15 over 14 / y-5 over 4y - I know you have to multiply by the reciprical of y-5 over 4y, but I just can't get the rest of it.
81a^2 over 2a^2-12a+18 times 2a-6 over 9a - I know on this one I got as far as
(81a^2)(2a-6)over 2(a-3)(a-3) I know I have to take it down more but I can't figure it out.
x-1 over x-7 minus x+1 over x+7 plus x-91 over x^2-49. I found the LCD of (x-7)(x+7) and it has to be multiplied to the first to parts of the equation. Where I am having a problem is with the x-91.
Answer by JenniferTutors(83) About Me  (Show Source):
You can put this solution on YOUR website!
Ok, for the first part, 3y-15 over 14 / y-5 over 4y.
Once you have those equations set up, after you do the reciprocal.. it should be 4y over y-5.
%283y-15%29%2F%2814%29x%284y%29%2F%28y-5%29

Next step, 3y-15, you can simplify that more by finding the lowest common factor between the two numbers. In this case, it's 3 because it can go into 15 and into itself.
So now, your problem would look like this:
3%28y-5%29%2F%2814%29x %284y%29%2F%28y-5%29
Looking at the problem now, we can simplify by crossing out the y-5 from both the top and bottom of the fractions.
Here's what it would look like next:
%283%29%2Across%28y-5%29%2F%2814%29x%284y%29%2Fcross%28y-5%29

Here's the next step if you're stuck from this point:
%2812y%29%2F%2814%29
You would multiply 3x4y to equal 12 which is still over 14. Simplify further by finding a common factor between the two numbers. Common factor would be 2, the answer = 6y%2F7
Now, for the next part:
%2881a%5E2%29%2F2%28a-3%29x%282a-6%29%2F%28a-3%29

Here, it's one of the same steps as before. Simplify by taking (2a-6) and finding the lowest common factor. In this equation, 2 is the only option because it can go into 6, and itself.

This is what the step would look like:
%2881a%5E2%29%2F2%28a-3%29x2%28a-3%29%2F%28a-3%29
Here, you can see that you can simplify further by crossing out the 2(a-3) from the top and the bottom.
This is what the step would look like:
%2881a%5E2%29%2F%28a-3%29

Now, you can't simplify any further.

The last equation you were asking about, the answer is x-91 because you can't do anything with it, in all of the steps in the problem after simplifying everything, you're left with x-91.