SOLUTION: I am struggling with this problem and do not know how to solve it. Please help if you can.. I am not to good at this type of problem and do not know where to begin. Thank you and t

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: I am struggling with this problem and do not know how to solve it. Please help if you can.. I am not to good at this type of problem and do not know where to begin. Thank you and t      Log On


   



Question 188743: I am struggling with this problem and do not know how to solve it. Please help if you can.. I am not to good at this type of problem and do not know where to begin. Thank you and this is a fraction over fraction and I need to simplify
%282%2F%28x%2B5%29%2B4%2F%28x%2B3%29%29%2F%28%283x%2B13%29%2F%28x%5E2%2B8x%2B15%29%29

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!

%282%2F%28x%2B5%29%2B4%2F%28x%2B3%29%29%2F%28%283x%2B13%29%2F%28x%5E2%2B8x%2B15%29%29

Write it as a division problem:

%282%2F%28x%2B5%29%2B4%2F%28x%2B3%29%29÷%28%283x%2B13%29%2F%28x%5E2%2B8x%2B15%29%29

Invert what we are dividing by, called the "divisor",
and change the division to multiplication, use as 
askerisk " * " for multiplication rather than an " x " 
so we won't get it mixed up with the x's used for
variables:

%282%2F%28x%2B5%29%2B4%2F%28x%2B3%29%29*%28%28x%5E2%2B8x%2B15%29%2F%283x%2B13%29%29

Let's just work on the part in the red rectangle below, and
just bring the rest down until we finish that part:

%28highlight%282%2F%28x%2B5%29%2B4%2F%28x%2B3%29%29%29*%28%28x%5E2%2B8x%2B15%29%2F%283x%2B13%29%29

The LCD in that part is %28x%2B5%29%28x%2B3%29, so we multiply the first
fraction by %28x%2B3%29%2F%28x%2B3%29 and the second fraction by 
%28x%2B5%29%2F%28x%2B5%29

*%28%28x%5E2%2B8x%2B15%29%2F%283x%2B13%29%29

In each term, indicate the multiplication of the 
numerators and denominators by writing them as one 
fraction:

*%28%28x%5E2%2B8x%2B15%29%2F%283x%2B13%29%29

Next we multiply out the numerators 
(but not the denominators):

*%28%28x%5E2%2B8x%2B15%29%2F%283x%2B13%29%29

Now we combine the numerators over the LCD:

%28highlight%28%28++6x%2B26++%29%2F%28%28x%2B3%29%28x%2B5%29%29++%29%29%29*%28%28x%5E2%2B8x%2B15%29%2F%283x%2B13%29%29

Now we can factor out a 2 in the numerator:

%28highlight%28%28++2%283x%2B13%29++%29%2F%28%28x%2B3%29%28x%2B5%29%29++%29%29%29*%28%28x%5E2%2B8x%2B15%29%2F%283x%2B13%29%29

That's all we can do with that part, so let's
put a red rectangle around the other part:

%28%28++2%283x%2B13%29++%29%2F%28%28x%2B3%29%28x%2B5%29%29++%29%29*%28highlight%28%28x%5E2%2B8x%2B15%29%2F%283x%2B13%29%29%29

We can factor the numerator:

%28%28++2%283x%2B13%29++%29%2F%28%28x%2B3%29%28x%2B5%29%29++%29%29*%28highlight%28%28%28x%2B3%29%28x%2B5%29%29%2F%283x%2B13%29%29%29

Next we indicate the multiplication of the numerators
and denominators:

%282%283x%2B13%29%28x%2B3%29%28x%2B5%29%29%2F%28%28x%2B3%29%28x%2B5%29%283x%2B13%29%29

We can cancel the %283x%2B13%29's



We can cancel the %28x%2B3%29's



We can cancel the %28x%2B5%29's



and we are left with just the number

2.

All that work just to get 2!  

Edwin