SOLUTION: Simplify {{{((4d^2)/(5d^2-30d+45))((5d-15)/(2d))}}}

Algebra ->  Graphs -> SOLUTION: Simplify {{{((4d^2)/(5d^2-30d+45))((5d-15)/(2d))}}}       Log On


   

Question 131889: Simplify %28%284d%5E2%29%2F%285d%5E2-30d%2B45%29%29%28%285d-15%29%2F%282d%29%29
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28%284d%5E2%29%2F%285d%5E2-30d%2B45%29%29%28%285d-15%29%2F%282d%29%29 Start with the given expression

%28%282%2A2%2Ad%2Ad%29%2F%285d%5E2-30d%2B45%29%29%28%285d-15%29%2F%282d%29%29 Factor 4d%5E2 to get 2%2A2%2Ad%2Ad

%28%282%2A2%2Ad%2Ad%29%2F%285%28d-3%29%28d-3%29%29%29%28%285d-15%29%2F%282d%29%29 Factor 5d%5E2-30d%2B45 to get 5%28d-3%29%28d-3%29

%28%282%2A2%2Ad%2Ad%29%2F%285%28d-3%29%28d-3%29%29%29%28%285%28d-3%29%29%2F%282d%29%29 Factor 5d-15 to get 5%28d-3%29

%28%282%2A2%2Ad%2Ad%29%2F%285%28d-3%29%28d-3%29%29%29%28%285%28d-3%29%29%2F%282%28d%29%29%29 Factor 2d to get 2%28d%29


%282%2A2%2Ad%2Ad%295%28d-3%29%2F%285%28d-3%29%28d-3%292%28d%29%29 Combine the fractions


Cancel like terms


%282d%29%2F%28d-3%29 Simplify



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Answer:


So %28%284d%5E2%29%2F%285d%5E2-30d%2B45%29%29%28%285d-15%29%2F%282d%29%29 simplifies to %282d%29%2F%28d-3%29

In other words, %28%284d%5E2%29%2F%285d%5E2-30d%2B45%29%29%28%285d-15%29%2F%282d%29%29=%282d%29%2F%28d-3%29