document.write( "Question 992884: What is the difference of the rational expressions below?
\n" ); document.write( "2x/x+3-4/x \n" ); document.write( "

Algebra.Com's Answer #612354 by jim_thompson5910(35256) $\"\"$ $\"About$

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Note: the LCD is $\"x%28x%2B3%29\"$ . In order to combine these fractions, we must get each denominator equal to the LCD.\r
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Step Number	Statement	Reason/explanation for given step
1	$\"%282x%29%2F%28x%2B3%29-4%2Fx\"$	Original expression (no reason needed)
2	$\"%28x%2Fx%29%2A%28%282x%29%2F%28x%2B3%29%29-4%2Fx\"$	Multiply the first fraction by $\"x%2Fx\"$
3	$\"%28x%2A2x%29%2F%28x%2A%28x%2B3%29%29-4%2Fx\"$	Use the idea that $\"%28x%2Fy%29%2A%28z%2Fw%29+=+%28x%2Az%29%2F%28y%2Aw%29\"$
4	$\"%282x%5E2%29%2F%28x%2A%28x%2B3%29%29-4%2Fx\"$	$\"x%2A2x\"$ becomes $\"2x%5E2\"$
5	$\"%282x%5E2%29%2F%28x%2A%28x%2B3%29%29-%284%2Fx%29%2A%28%28x%2B3%29%2F%28x%2B3%29%29\"$	Multiply the second fraction by $\"%28x%2B3%29%2F%28x%2B3%29\"$
6	$\"%282x%5E2%29%2F%28x%2A%28x%2B3%29%29-%284%28x%2B3%29%29%2F%28x%28x%2B3%29%29\"$	Use the idea that $\"%28x%2Fy%29%2A%28z%2Fw%29+=+%28x%2Az%29%2F%28y%2Aw%29\"$
7	$\"%282x%5E2-4%28x%2B3%29%29%2F%28x%28x%2B3%29%29\"$	Use the idea that $\"a%2Fd-b%2Fd=%28a-b%29%2Fd\"$ (notice the common denominator d)
8	$\"%282x%5E2-4x-12%29%2F%28x%28x%2B3%29%29\"$	Distribute

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\n" ); document.write( "\n" ); document.write( "Final Answer: $\"%282x%5E2-4x-12%29%2F%28x%28x%2B3%29%29\"$ \r
\n" ); document.write( "\n" ); document.write( "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 $\"%282x%5E2-4x-12%29%2F%28x%5E2%2B3x%29\"$
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