SOLUTION: Subtract the fractions: [2/(5w + 10)] - [3/(2w - 4)]

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Question 147258: Subtract the fractions:
[2/(5w + 10)] - [3/(2w - 4)]
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2%2F%285w+%2B+10%29+-+3%2F%282w+-+4%29 Start with the given expression.

2%2F%285%28w+%2B+2%29%29+-+3%2F%282%28w+-+2%29%29 Factor the denominators.


Multiply the first term 2%2F%285%28w+%2B+2%29%29 by %282%28w-2%29%29%2F%282%28w-2%29%29.


%284%28w-2%29%29%2F%2810%28w+%2B+2%29%28w+-+2%29%29+-+3%2F%282%28w+-+2%29%29 Combine and multiply the fractions.


Multiply the second term 3%2F%282%28w+-+2%29%29 by %285%28w%2B2%29%29%2F%285%28w%2B2%29%29.


Combine and multiply the fractions.


%284%28w-2%29-15%28w%2B2%29%29%2F%2810%28w+%2B+2%29%28w+-+2%29%29 Since the denominators are now equal, we can combine the numerators over the common denominator.


%284w-8-15w-30%29%2F%2810%28w+%2B+2%29%28w+-+2%29%29 Distribute.


%28-11w-38%29%2F%2810%28w+%2B+2%29%28w+-+2%29%29 Combine like terms.


%28-11w-38%29%2F%2810%28w%5E2-4%29%29 Foil %28w+%2B+2%29%28w+-+2%29 to get w%5E2-4


%28-11w-38%29%2F%2810w%5E2-40%29 Distribute


So 2%2F%285w+%2B+10%29+-+3%2F%282w+-+4%29 simplifies to %28-11w-38%29%2F%2810w%5E2-40%29


In other words, 2%2F%285w+%2B+10%29+-+3%2F%282w+-+4%29=%28-11w-38%29%2F%2810w%5E2-40%29