SOLUTION: can you please help me answer: {{{((x^2+5x+4)/(x+1))/((x+3)^2/(x^2-9))}}} or {{{(x^2+5x+4)/(x+1)}}}÷{{{(x+3)^2/(x^2-9)}}}

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: can you please help me answer: {{{((x^2+5x+4)/(x+1))/((x+3)^2/(x^2-9))}}} or {{{(x^2+5x+4)/(x+1)}}}÷{{{(x+3)^2/(x^2-9)}}}      Log On


   

Question 152480This question is from textbook Algebra structure and method book 1
: can you please help me answer: %28%28x%5E2%2B5x%2B4%29%2F%28x%2B1%29%29%2F%28%28x%2B3%29%5E2%2F%28x%5E2-9%29%29 or
%28x%5E2%2B5x%2B4%29%2F%28x%2B1%29÷%28x%2B3%29%5E2%2F%28x%5E2-9%29 This question is from textbook Algebra structure and method book 1

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28x%5E2%2B5x%2B4%29%2F%28x%2B1%29%29%2F%28%28x%2B3%29%5E2%2F%28x%5E2-9%29%29 or
%28x%5E2%2B5x%2B4%29%2F%28x%2B1%29÷%28x%2B3%29%5E2%2F%28x%5E2-9%29

Invert the second fraction and change the
division to multiplication:

%28x%5E2%2B5x%2B4%29%2F%28x%2B1%29×%28x%5E2-9%29%2F%28x%2B3%29%5E2

Factor the two numerators, and write %28x%2B3%29%5E2 as %28x%2B3%29%28x%2B3%29

%28%28x%2B4%29%28x%2B1%29%29%2F%28x%2B1%29×%28%28x-3%29%28x%2B3%29%29%2F%28x%2B3%29%28x%2B3%29

Put parentheses around the left denominator so
everything will be "packaged" in parentheses:

%28%28x%2B4%29%28x%2B1%29%29%2F%28%28x%2B1%29%29×%28%28x-3%29%28x%2B3%29%29%2F%28x%2B3%29%28x%2B3%29

Indicate the multiplication of the numerators 
and denominators, so it will all be one fraction:

%28%28x%2B4%29%28x%2B1%29%28x-3%29%28x%2B3%29%29%2F%28%28x%2B1%29%28x%2B3%29%28x%2B3%29%29 

Cancel the %28x%2B1%29's

 

Cancel the %28x%2B3%29 in the top with one of the
%28x%2B3%29's in the bottom:



All that's left is

%28%28x%2B4%29%28x-3%29%29%2F%28x%2B3%29

You can leave it like that, or if you like
you can FOIL out the top as x%5E2%2Bx-12
and leave it this way:

%28x%5E2%2Bx-12%29%2F%28x%2B3%29

Edwin