Question 203063
{{{(15ab/4)}}}*{{{(8/9a^2b^2)}}}


I won't know how to put this in nice fractions for you, so I'll explain, as best as I can, what I'm doing............


{{{(15ab/4)}}}*{{{(8/9a^2b^2)}}} 


The 15 and the 9 can each be reduced when divided by 3.  They become 5 and 3.
The 4 and the 8 can each be reduced when divided by 4. They become 1 and 2
The ab in the numerator can be canceled, but that changes the {{{a^2}}} and the {{{b^2}}} in the denominator to:   {{{ab}}}


SO when we reduce and cancel, we get:


{{{(5)*(2)}}}/{{{(1)*(3)ab}}}  .........OR.........

{{{10/3ab}}}


NEXT QUESTION:


{{{(6a/8b)/(10c/12d)}}} 


The above is how I am reading your question.  If I am correct, then we would do that problem the way we would do any division problem when we work with fractions.  In other words, when you divide with a fraction, you MULTIPLY by the reciprocal.  So your problem is now........


{{{(6a/8b)}}}*{{{(12d/10c)}}}


The 6 and the 10 can be reduced when divided by 2. They become 3 and 5.
The 12 and the 8 can be reduced when divided by 4. They become 3 and 2.


Your problem is now............


{{{(3a/2b)}}}*{{{(3d/5c)}}} and this is:


{{{9ad/10bc}}}


NEXT QUESTION:  



{{{2x^2 + x - 3}}}/{{{9}}}*{{{(x +1)^2}}}/{{{2x^2 + 5x + 3}}}


If I have written your problem correctly, then it can be factored like this:


{{{(2x + 3)(x-1)(x + 1)(x + 1)}}}/{{{(9)(2x + 3)(x + 1)}}}


So the (2x + 3) in the numerator can be canceled with the (2x+3) in the denominator.
The (x + 1) in the numerator can be canceled with the (x + 1) in the denominator.


That leaves you with:


{{{(x - 1)(x + 1)/9}}}



I am sorry to say that your last problem I don't think I'm seeing correctly.  Can you repost it, please?   It's this part of the problem I'm not sure about: 

(1/25-y^2)


I am not sure you have written it correctly.  The second part is easily factored.  The (6 - 3y) can be factored to 3(2 - y) and the {{{y^2-7y+10}}} can be easily factored to (y-5)(y-2).   I just am not certain your first part of the problem is written correctly.


I hope this helps .......