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 -

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) (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.
x

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:
x
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:
x

Here's the next step if you're stuck from this point:

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 =
Now, for the next part:
x

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:
x
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:

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.

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