SOLUTION: Find the indicated products and quotients. 1. (9z^3/16xy)(4x/27z^3) 2. (3m-9/4m+8)(m^2+5m+6/m^2-9) 3. (y^2+3y-10/3y+15) / (10-5y) Thanks

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Question 202559: Find the indicated products and quotients.
1. (9z^3/16xy)(4x/27z^3)
2. (3m-9/4m+8)(m^2+5m+6/m^2-9)
3. (y^2+3y-10/3y+15) / (10-5y)
Thanks

Answer by PRMath(133) (Show Source):
You can put this solution on YOUR website!
1. (9z^3/16xy)(4x/27z^3)
2. (3m-9/4m+8)(m^2+5m+6/m^2-9)
3. (y^2+3y-10/3y+15) / (10-5y)

Before we do these, we have to agree that

Further, we have to agree that

Those are good facts to have in your mind, so let's begin.

1. (9z^3/16xy)(4x/27z^3)

I read this as: *

Because you are multiplying, you can factor terms, just like we did above when we said

SO - let's factor:

The 9 in the numerator can be factored into the 27 of the denominator to give you

The 4 in the numerator can be factored into the 16 of the denominator to give you

The in the numerator can be factored into the of the denominator to give you

The "x" in the numerator can be factored into the x of the denominator to again give you

What you have left is:

which is:

2. (3m-9/4m+8)(m^2+5m+6/m^2-9)

Let's just break this down piece by piece, because it may be quicker:

Numerator of first fraction: 3m - 9
Let's factor out 3: 3(m-3)

Denominator of first fraction: 4m + 8
Let's factor out 4: 4(m + 2)

Numerator of 2nd fraction:
Let's factor this to be: (m+2)(m+3)

Denominator:
Let's factor this to be: (m+3)(m-3)

NOW we have:

NOW factor out

What you have left is

3.(y^2+3y-10/3y+15) / (10-5y)

Numerator of first fraction:
Factor to: (y+5)(y-2)

Denominator of first fraction:3y+15
Let's factor that to: 3(y+5)

Second fraction: 10-5y
Factor to: 5(2-y)

Now we have:

(y+5) can factor out of the numerator and denominator so we have left....

I hope this helps. :-)