SOLUTION: {{{(((5w^2-27w+10)/(5w^2+23w-10))) / (((25w^2-20w+4)/(5w^2+23w-10)))}}}

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: {{{(((5w^2-27w+10)/(5w^2+23w-10))) / (((25w^2-20w+4)/(5w^2+23w-10)))}}}      Log On


   

Question 626234:
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
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Write as the division of two fractions:

 %28%285w%5E2-27w%2B10%29%2F%285w%5E2%2B23w-10%29%29%22%F7%22%28%2825w%5E2-20w%2B4%29%2F%285w%5E2%2B23w-10%29%29 = 

Invert the second fraction and change division to multiplication:

%28%285w%5E2-27w%2B10%29%2F%285w%5E2%2B23w-10%29%29%22%D7%22%28%285w%5E2%2B23w-10%29%2F%2825w%5E2-20w%2B4%29%29 = 

Factor all numerators and denominators:

%28%28%28w-5%29%285w-2%29%29%2F%28%285w-2%29%28w%2B5%29%29%29%22%D7%22%28%285w-2%29%28w%2B5%29%29%2F%28%285w-2%29%285w-2%29%29%29 =

Cancel a pair of (5w-2)'s:

%28%28%28w-5%29%28cross%285w-2%29%29%29%2F%28%28cross%285w-2%29%29%28w%2B5%29%29%29%22%D7%22%28%285w-2%29%28w%2B5%29%29%2F%28%285w-2%29%285w-2%29%29%29 =

Cancel the (w+5)'s:

%22%D7%22%28%285w-2%29%28cross%28w%2B5%29%29%29%2F%28%285w-2%29%285w-2%29%29%29 =

Cancel another pair of (5w-2)'s:

%22%D7%22%28%28cross%285w-2%29%29%28cross%28w%2B5%29%29%29%2F%28%28cross%285w-2%29%29%285w-2%29%29%29 =

All that's left is:

%28w-5%29%2F%285w-2%29

Edwin