SOLUTION: Simplify {{{((-12+2w)/5)/((49w-294)/25)}}}

Algebra ->  Algebra  -> Rational-functions -> SOLUTION: Simplify {{{((-12+2w)/5)/((49w-294)/25)}}}       Log On

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Question 125840: Simplify

%28%28-12%2B2w%29%2F5%29%2F%28%2849w-294%29%2F25%29
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28-12%2B2w%29%2F5%29%2F%28%2849w-294%29%2F25%29 Start with the given expression

%28%28-12%2B2w%29%2F5%29%2A%28%2825%29%2F%2849w-294%29%29 Multiply the first fraction by the reciprocal of the second fraction


%28%282%28w-6%29%29%2F%285%29%29%28%2825%29%2F%2849w-294%29%29 Factor -12%2B2w to get 2%28-6%2Bw%29 and rearrange the inner terms to get 2%28w-6%29


%28%282%28w-6%29%29%2F%285%29%29%28%285%2A5%29%2F%2849w-294%29%29 Factor 25 to get 5%2A5

%28%282%28w-6%29%29%2F%285%29%29%28%285%2A5%29%2F%2849%28w-6%29%29%29 Factor 49w-294 to get 49%28w-6%29


2%28w-6%29%285%2A5%29%2F5%2849%28w-6%29%29 Combine the fractions


2cross%28%28w-6%29%29%28cross%285%29%2A5%29%2Fcross%285%29%2849cross%28%28w-6%29%29%29 Cancel like terms


%282%2A5%29%2F49 Simplify


10%2F49 Multiply



So %28%28-12%2B2w%29%2F5%29%2F%28%2849w-294%29%2F25%29 simplifies to 10%2F49


In other words, %28%28-12%2B2w%29%2F5%29%2F%28%2849w-294%29%2F25%29=10%2F49