Express as a single term: 1/2x+1 - x/x-1

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In summary, to express 1/2x+1 - x/x-1 as a single term, you first need to find a common denominator for the two fractions. This allows for easier simplification and identification of patterns within the expression. After it is expressed as a single term, it can still be further simplified using algebraic techniques. To check if it has been correctly expressed, you can expand it back to its original form or try simplifying it further. Other methods of expressing this expression as a single term include using the LCD and converting all fractions to decimals.
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davie08
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Homework Statement



express as a single term: 1/2x+1 - x/x-1

Homework Equations



it says to bring to a common denominator

The Attempt at a Solution



I think I should take out an x-1 but I forget where to go from there. I will be posting a lot of questions this is a review for my test tomorrow that i forgot about.
 
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  • #2
multiply the first term by (x-1)/(x-1) and the second by (2x+1/2x+1)
 
  • #3
thanks.
 

FAQ: Express as a single term: 1/2x+1 - x/x-1

What is the process for expressing 1/2x+1 - x/x-1 as a single term?

To express 1/2x+1 - x/x-1 as a single term, you need to first find a common denominator for the two fractions. In this case, the common denominator is x(x-1). Then, you can combine the numerators and factor out the common denominator, resulting in a single term.

Why is it important to express this expression as a single term?

Expressing an expression as a single term allows for easier simplification and mathematical operations. It also makes it easier to identify patterns and relationships within the expression.

Can this expression be simplified further after it is expressed as a single term?

Yes, after expressing the expression as a single term, you can use algebraic techniques such as factoring or combining like terms to simplify it further.

How can I check if I have correctly expressed this expression as a single term?

To check if you have correctly expressed the expression as a single term, you can expand the expression back to its original form and see if it matches the original expression. You can also try simplifying the expression further and see if you get the same result.

Are there any other ways to express 1/2x+1 - x/x-1 as a single term?

Yes, there are multiple ways to express this expression as a single term. Some other common methods include using the LCD (Least Common Denominator) and converting all the fractions to decimals before combining them into a single term.

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