SOLUTION: What is the difference of the rational expressions below? 2x/x+3-4/x

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Question 992884: What is the difference of the rational expressions below?
2x/x+3-4/x
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Note: the LCD is x%28x%2B3%29. In order to combine these fractions, we must get each denominator equal to the LCD.
Step NumberStatementReason/explanation for given step
1%282x%29%2F%28x%2B3%29-4%2FxOriginal expression (no reason needed)
2%28x%2Fx%29%2A%28%282x%29%2F%28x%2B3%29%29-4%2FxMultiply the first fraction by x%2Fx
3%28x%2A2x%29%2F%28x%2A%28x%2B3%29%29-4%2FxUse the idea that %28x%2Fy%29%2A%28z%2Fw%29+=+%28x%2Az%29%2F%28y%2Aw%29
4%282x%5E2%29%2F%28x%2A%28x%2B3%29%29-4%2Fxx%2A2x becomes 2x%5E2
5%282x%5E2%29%2F%28x%2A%28x%2B3%29%29-%284%2Fx%29%2A%28%28x%2B3%29%2F%28x%2B3%29%29Multiply the second fraction by %28x%2B3%29%2F%28x%2B3%29
6%282x%5E2%29%2F%28x%2A%28x%2B3%29%29-%284%28x%2B3%29%29%2F%28x%28x%2B3%29%29Use the idea that %28x%2Fy%29%2A%28z%2Fw%29+=+%28x%2Az%29%2F%28y%2Aw%29
7%282x%5E2-4%28x%2B3%29%29%2F%28x%28x%2B3%29%29Use the idea that a%2Fd-b%2Fd=%28a-b%29%2Fd (notice the common denominator d)
8%282x%5E2-4x-12%29%2F%28x%28x%2B3%29%29Distribute

Final Answer: %282x%5E2-4x-12%29%2F%28x%28x%2B3%29%29
Note: an optional step is to distribute in the denominator turning x%28x%2B3%29 into x%5E2%2B3x. So an alternative equivalent answer is %282x%5E2-4x-12%29%2F%28x%5E2%2B3x%29